One of Robert Jordan's answers to the Question of the Week (week 9, 2nd series) at the Tor website said:

~quote~~ "A channeler sees the flows as colored very faintly, according to which of the Five Powers is involved (red = Fire, Blue = Water, green = Earth, yellow = Air, white = Spirit), although the "feel" of the flows are also different to a channeler, so that a channeler can tell one from another without actually seeing them. (That is how someone can tell that somebody else has channeled, say, Fire and Earth, in their vicinity without seeing the flows.) It isn't a physical feel; you might almost as well say that they have different flavors. They appear to be smooth and nearly transparent, tinged with color."

Now, every channeler would associate these colors with the respective specific OP flows. Aes Sedai have a very stable and universal (i.e. the same for every channeler) system of associations for five of the basic colors. Only a more popular and stable color symbolism system from before the mass usage of channeling could outweigh this natural symbolism system, and we have no indication that any another such colour symbolism system exists.

Five of the seven Ajahs have the colors of the flows of One Power. Can this be an accident? So, why do the Ajahs have their specific colors?

One of the traditional (and the only known for sure) associations of the elemental flows is that Air and Water are the powers of women, and Fire and Earth the powers of men. This association is obvious from the widespread Aes Sedai saying that Water and Air can win over any Fire and Earth and that it means that they believe that female channelers have some advantages over the male ones. Further, Moiraine explicitly mentions the male channelers being stronger in Fire and Earth. This is a kind of knowledge that for some reason was never forgotten during all the 3000 years without researchable male channelers. Among these four powers, Air is especially closely associated with women, and Fire with men (I base this on the title of the book, Loial mentions as the best one about male and female channeling: an early Ogier work entitled Men of Fire and Women of Air ).

So the corresponding colors would

Red (Fire): in first place related to men

Green (Earth): in second place related to men

Yellow (Air): in first place related to women

Blue (Water): in second place related to women

A possible reason for Fire to be considered male element before Earth and Air as female before Water, is maybe that Air and Fire are more easily and frequently used than Earth and Water. Among AS only few have Talent to work with Earth, while never any Talents required for Fire are mentioned. Asha'man often use Air, but they seem to have less familiarity with Water weaves. Even women seem to use Water not so ofter as Air, and men use Earth not so ofter as Fire. That could easily create the tacit ranking of Air and Fire before Water and Earth. However the second place for Earth and Water is not a primary statement of my theory.

The "male/female" association of green, blue and especially red and yellow, is, in contrast to all other interpretations, not just something those old-time Aes Sedai maybe thought, but something we are completely sure they associated with the said colors. When an Aes Sedai thinks about Fire and Earth, she will think about them as the "male" powers, even if she personally likes to use them very much and is talented with them. This male-female association is the only symbolism about the powers for which we have proof. So even if the original intentions of the Ajah founders were something else, they had to also consider the "male-female" meaning and symbolism of the Ajah color, because everybody will associate this meaning with the color. It's like if I today founded a movement and chose the swastika as it's symbol - I could argue that this swastika expresses the true, original, ancient Hindu meaning of the symbol, that it has nothing to do with any kind of Nazis, and I may have excellent reasons for that, but whatever I do, everybody will make a connection between the symbol of my movement and the Nazis, so that I'll have to take that into account if I'm not totally blind. The same with the Ajah colors: the founders of an Ajah may want to express anything, but they will also know, that the other Aes Sedai will connect the color with the respective male/female meaning. So any Ajah choosing one of the colors red, yellow, green or blue will expect that the other Aes Sedai connect their identity with the respective male or female channeling symbolism.

Now, it is interesting that both the Red and the Green Ajahs are the Ajahs that include dealing with men as their official missions. No other Ajahs are officially focused on men. The Red are especially concentrated on men, and, more specifically on channeling men, while the Greens are known to have the completely opposite opinion about men in general. They are polar opposites on the issue of men and in their reactions to the events of the Breaking. The Reds react to the immediate effect of the taint on men, the Greens, as alternative to the Reds, prepare for the final consequence of the events of the Age of Legend's end, and these final events are centered around one very special channeling man - the Dragon reborn. So the connection between the Red and Green and the male channeling is visible.

If this interpretation is correct, the Yellow and the Blue Ajahs must originally have declared their roles as the Ajahs primarily connected to female channeling as opposed to male channeling. Why would this be the case with them and especially with the Yellow Ajah with it's focus on Healing?

It's about the political situation of the Aes Sedai in the early post-breaking time. The people blamed for the Breaking not only the male channelers, but all Aes Sedai. That may be irrational and stupid, but it is fact. In the books we have PoVs of people from that time that explicitly think that Aes Sedai, including the female Aes Sedai, are responsible for the Breaking, and they must be killed for that. And these people are not only the few extremists like the current Whitecloaks, but I have impression, they were the vast majority of the population. The fact that in these days rulers have to keep their Aes Sedai advisors secret, means that population hate any As Sedai, and in the earliest days it was not because of their reputation as political manipulators, because in those days there was no White Tower yet, but only a diffuse ocean of ajahs and separate channelers. Lot of people after the Breaking wanted a world without any kind of Aes Sedai. This was one of the primary political issues for the new-founded Tower.

Every faction of the founders of the Tower had to consider a plan to justify the existence of an official Aes Sedai organization in the eyes of the world. To justify the role of the Tower is to define the reason why the world needs the Tower. Now we see that the different Ajahs define the main role of the Tower in different ways. Actually that is the official difference between the ideals of the seven particular Ajahs. Because this was the primordial issue for the beginning of the Tower, it is safe to state that it was the topic about which the original seven Ajah officially disagreed and disputed between each other. So that is likely to be the main thing an Ajah had to express through its self-image and identity: the Ajah's opinion about the official role of the whole Tower. The specialization of every Ajah was rather a consequence of what the initial ajahs stressed as their variant of the main message of the Tower. The seven colors have meaning as old as conscious channeling is, but in the moment of creation of the Tower these meanings were applied to the specific situation of the moment, and after the Tower begun to exist, these early specifications became a tradition and the original choosing of colors was forgoten.

Now one of the most obvious ways to plan to win back the trust of the world in Aes Sedai, is to make it obvious to the world that these Aes Sedai are absolutely different from those male Aes Sedai who broke the world, and to make it obvious for the world that the world needs the good Aes Sedai. How is that to be achieved? People want no gifts from Aes Sedai, and it is not possible for the Aes Sedai to give the world any of the goodies from the Age of Legends. People during the Breaking found ways to survive and that made these people feel independent, and they would be pretty much against any attempts of the Tower to make them dependent. They would not accept any goodies from the Aes Sedai, even if the Aes Sedai can give them such. Reds would claim that they are needed to capture the male channelers, but the world would prefer to kill all the Aes Sedai, so even the Red activity will not make the Aes Sedai trusted: they would use Aes Sedai as allies to fight the channelling men, and after that will fight the Aes Sedai, because they're also distrusted. But now there is something that Aes Sedai still can do and that even the people who hate Aes Sedai need sometimes: sometimes people need medical care. Even in the late Third Age, a lot of people prefer to suffer rather than be Healed by an Aes Sedai, but sometimes the disease gets too dangerous, sometimes it threatens with very unpleasant death, and that can weaken a lot of resolve. Healing is something that Aes Sedai can consider the world will accept from Aes Sedai despite all the hatred.

So it is to be expected that some of the founders of the Tower will announce Healing as the main image of the Tower for the eyes of the world. The message would be something like: "We are not those who broke the world, but we are those who Heal you; we are not those who threaten your life, but we are those who save your life". Healing becomes a slogan, an advertisement for the whole White Tower to win the world's trust. Because one of the purposes of this slogan is to make the difference between the new Tower = the legitimate female Aes Sedai, from those who broke the world and therefore who are to be hated = the male Aes Sedai, so it's logical, that the Aes Sedai faction proposing this slogan would use symbolism designating them as female in difference to male channelers ("We are not like those awful male channelers, we are totally different, look at what the men did, and at what we, women, do now" ).

This is also corroborated by the fact that the Yellow Ajah have for so long a time so stubbornly maintained the idea that Healing is to use only Air, Water and Spirit: could it be that purely ideological and symbolical gestures determined the neglect of all-flows healing? Could it be, that some early Yellows, wanting to make a symbolical gesture, declare that they will not use that "damned male Fire and Earth" for so important an action as Healing? Could the reduction of Healing capability be a result of somebody's stupid idea of making propaganda?

Apropos I'm not stating that there was a dedicated group of Healers in difference to other ajahs, who picked up the color of Air. I'm stating that the group that chose the color of Air and later they became, as a consequence of their choice, a faction of designated Healers. In the momend of the choosing the Yellow color the ajah was the ajah of those who's first care was the good reputation of the Aes Sedai in the eyes of the world, and in the circumstances this task required stress on Healing.

Reds did something different: their message was that there is still a danger in the world, and the world needs reliable and powerful and organized Aes Sedai to fight this danger. So the symbolism of the Red Ajah has the message "Do not forget about the danger of channeling men!". Fire can be also associated with Purge - the Red Ajah cleansing the world from male channellers. Also Fire is a power daily used by Aes Sedai for turning lights on. Turning lights on is symbolically close to putting all the dirty secrets into an open, i.e. purge again. The Reds are the seekers, who (symbolically) go through the worlds with bright torches to seek for dangers and to burn them away.

I'll suppose that the Yellow and the Red proclamations were the first two ones the Tower declared as the official advertising of the Tower's role in the world. For example, the Grey dedication to mediation of conflict is also a good role for the Tower, but for it to be accepted in the world, at least some bit of trust is required: nobody will accept a peacemaker whom everybody hates to death. Greens are focussed on a very distant event - the Last battle - so they also first need the Tower in general to be accepted for their role to be accepted also. After that they may stress the future danger of the Last Battle (a danger like the message of the Reds), and also connected to men (the Dragon is a male channeler), so they have also the symbolism of "Remember the danger!", i.e. the alternative male color.

Also Earth is of the first importance in all weaves for building and forging architectural objects and metal artefacts. If a fortress or an arsenal is to be built, the symbolic color for a channeler to do this task, will be Green. Preparing for great battle in the future is building fortifications, forging weapons (both Earth-connected, although as far as weapons are concerned, the second Oath had not yet been introduced in these early times) and gathering and training army (for which a fortified central base and good arsenal is a prerequisite). So Green would be the color for preparing for a great battle. Fire is the power used in immediate fight, a fight that goes on right now: that is the Red strategy. The Green are those who don't fight right now, but prepare to a battle in the future.

While Blues were also active from the beginning, they also needed some little trust before having a high profile, so they also would declare their color after the Red and Yellow. The Blues would be the ones with daily missions, although not stressing the danger of channelling men, and they also would need very much the notion of the radical difference of the female Aes Sedai against the bad male ones: so they pick up the second female color as their symbol.

According to this pattern the Blue must mean the alternative to the direct approach of the Yellows. I guess that the Blue idea refers the ideology of Latra Posae's faction. The initial Blues maybe claimed that they were the true followers of those Female Aes Sedai who met the problems of the early Breaking and followed their political style. We see from the Rhuidean memories that these Aes Sedai were concentrated on the pragmatic missions of doing what must be done, without relying on grand preparations and activity, but rather by precise silent best-effort actions.

White is the symbol of "spirit" and according to that, the White Ajah has a purely "spiritual" dedication. Usually spiritual dedication is associated with self-control and thus to some ascetics, and "serious", "ideal" things as the only worthwhile things to think about (like philosophy and truth). Such association with serious subtle contemplation may be the reason that the novices, gai'shain, and mourning people also wear white.

The Grey and the Brown Ajahs have colors not present in the visual appearance of channeling. Both seem also to be symbolically neutral colors. The Greys definitely would claim to take no part in the ideological controversy between the five bright-colored Ajahs. The Greys are dedicated to mediate between groups of different ideologies. The Browns also would rather declare that they take no part in the ideological disagreements. They claim to be objective beholders that do not take any part. So this Ajah uses the most neutral color in the symbolical system, a color that doesn't express mediation, but only inert position against any ideological position.

When we see a political faction declaring itself as being "neutral", or "independent", does it mean that this faction is intending to stay away of politics? Usually when a group identifies itself so, it has in mind concurrent political groups, whose pragmatic and ideology-free alternative they claim to be. By naming itself "neutral" a group often claims to perform the balance between other groups, to have some arbitrary role. Often that implies even more messing in political affairs than radical self-identification, but the ballancing group can be with full right be called "neutral" as compared with the radical wings. When speaking about the Grey being "neutral color I meant exactly this sense of "neutral".

That the Grey and Brown are exactly these colors is due to the fact that for WoTlanders the seven colors of the ajahs are the "basic colors". The reason for that is Robert Jordan's opinion that exactly these seven colors are the basic ones. As Jordan said in an interview:

Q: I was wondering how did you choose the colors for the ajahs, ie. why are some colors such as orange left out and gray is in. Thanx for answering my question.

A: I stuck with what you might call basic colors, and orange is not a basic color.

So, never mind what the basic colors are in the physiology of eye reception, the arts, in video technology etc., in WoT the basic colors are exactly those seven colors (+ black), not others. Because RJ said so.

Having all the "basic" colors, the seven Ajahs can consider themselves to represent the full scale of the variable positions for the White Tower and its main goals.

Addendum:

Ajahs and the colors on the Portal Stones

There is a popular opinion, that the Ajahs may chose their colors after the seven colors found on the Portal Stones. It is a theory I basically disagree with. I can see as possibly valid many other secondary meanings of the Ajah colors as additional meanings together with the primary male/female meaning, but I will insist that the Stone Colors have nothing to do with Ajah colors, that they are very unlikely to be able to influence the choice of Ajah colors, that it is very unlikely that even the AoLer Aes Sedai thought about the seven colors as the "colors from the Portal Stones", and that it is doubtfull that the Portal Stones had any importance for the Aes Sedai after the Breaking. The choice of exactly this set of colors in the both cases could be too easily attributed to the fact that for Jordan (as I proved above) these 7 colors are THE basic colors, i.e. this set of colors is simply "all the colors". Also Portal Stones details are hardly a convenient logo for a political organization. As Loial tells to Rand in tGH ch.13, the Mirror Worlds were explored only by some of the most powerfull of the few AoLer Aes Sedai who focussed their interest on Travelling between places (i.e. it was a relatively close circle of researchers). The quotes from old books Loial gives as examples, and that supposedly are derived from late Aoler manuscript, are written in a somewhat enigmatic for a causal observer style and have too much of a neutral agaist the world's events purely philosophical ramblings in it (...what will happen if a woman choses one way instead of another... and similar stuff). This doesn't seem like something usable for a political organization (that the White Tower with it's Ajahs is) to identify itself with. For me it looks like political factions designating themselves by terms borrowed from the quantum theory. Another problem is that in the Age of Legends it was unknown who (or what) created the portal Stones and how. If the seven colors were built together with the creation of the Stones themselves, then the AoLer AS couldn't know the meaning of these colors (so they couldn't have a Very Important Thery Borrowed from the Ancient, that to make the colors of the Stones a well-accepted doctrine). If the colored amphitheatral thing was added later in AoL to already existing, then the AS had to bring their own symbolic in it, a symbolic that may be not derived from the study of Portal Stones (There is no noticeable meaning of Colors in the usage of the Stones we know), but for different reasons (e.g. a logo of Collam Daan, or rhetorics of harmony of the all things, or just a decoration). It is also an open option that these colors where added in the Third Age by the White Tower in order to claim Tower's possession over these objects of Power, and so they would be after the already existing seven Ajahs. The fact that the first time we see these colors at the Stones (in tGH ch.13) Rand's impulsive reaction was the connection with the seven ajahs, is for me most likely Jordan's hint, that such connection doesn't exist. Because in this case Rand's reaction couldn't be based on any kind of knoweledge (even Lews Therin's memories couldn't help here, because LTT couldn't know anything about the "seven Ajahs") and is for him to express in a more acceptible form his horrifying suspect that the situation has to do with channeling and more specifically with his own unconscious channeling... If Portal Stones were so important for the early Aes Sedai of the third Age, so it would be very strange that the current Tower is so indefferent about the fate of these Stones. If the Ajahs chose their colors after the Stones, so they will praise these Stones high and they will claim them to be "Aes Sedai Places" and symbol of the Tower's dignity. That means that they would not them be in so pityfull state we find them now. The Aes Sedai would try to keep them in good order as symbols of their Ajahs. The Tower however shows nothing like that. The Tower shows rather apathy about the Portal Stones (except maybe some Brown sister who can be interested in any possible object of knowledge no matter is it a Portal Stone or a beetle). That seems to contradict to the supposed importance of the portal Stones for the Ajahs. In any case, Stones or no Stones, the OP-related symbolism of the colors still is there and would be more "natural" assotiation for any channeler than the sophisticated usage of colors on a particular artefact.