Is there any anecdotal evidence that Egwene is the reincarnation of a previous Amyrlin/Aes Sedai? Of course she would've been an extremely powerful channeler in past lives, but are any of her past lives hinted about? I have a suspicion about one of them, simply because how her battle with a certain Forsaken in AMoL went, but it's just speculation...
Anecdotal evidence, yes.
There are a few different theories about the previous lives of Egwene, and sometimes also Elayne and Nynaeve, based on possible hints dropped in various places in the books. Here are some of the ones I've found (with evidence for the theory bolded by me in each case):
Eldrene ay Ellan ay Carlan, the last Queen of Manetheren.
Since channeling is soul-related, this apparently means that someone who can channel will always be born into a body that has the right genetics for channeling. Following this logic, one can assume that in every incarnation she was an extremely powerful channeler. Is it just me or does the story of her life eerily parallel that of several past heroine Aes Sedai? Especially the Queen of Manetheren (in the top echelon of channeler strength during her lifetime, married to her royalty husband, Amrylin rival (Elaida) who was jealous of her strength, went berserk in battle when her husband/Warder was killed and drew in so much of the One Power that she killed herself and all of her enemies).
Deindre, an Aes Sedai of the Age of Legends.
I believe that we have already seen the characters of Egwene,Elayne and Nynaeve in their previous lives. In "The Shadow Rising" (chapter 26 "The dedicated") when Rand relives the history of the Aiel through his ancestors, specifically Jonai, there is an encounter with three Aes Sedai: Deindre, Oselle and Solinda. Could these be Egwene, Nynaeve and Elayne in their previous lives? I submit this theory for the following reasons:
Oselle has long dark hair and from the evidence is this chapter is ruled by her emotions. Nynaeve has long dark hair and as we know she has on numerous occaions been ruled by her emotions (in particular anger)
Deindre has dark eyes, is calm when dealing when dealing with Oselle and has the foretelling (Anaiya in "The Great Hunt" likens foretelling to dreaming). Egwene as we know has dark eyes and has the ability to dream. In "The Fires Of Heaven" she decides to adopt the approach of remaining cool when dealing with an irate Nynaeve as it seems to have the best results.This is the approach that Deindre takes when dealing with Oselle. Could this be significant?
Solinda has sun-red hair and is the peace-keeper between Deindre and Oselle. As we know, Elayne has red-gold hair and normally acts as the peace keeper between Nynaeve and Egwene (See "The Dragon Reborn").
[...] Apart from the shared traits and physical attributes there is always something significant about the number three in religion and myths. The three most important female channelers of this time that we know of are Egwene,Elayne and Nynaeve. They all have crucial roles to play in the build up to and after Tarmon Gai'don. I believe that the ancient Aes Sedai that we see through the eyes of Rand were crucial in the formation of The Eye of the World, which was one of the critical tasks during the breaking of the world, so could it not be these three in a previous existence.
Latra Posae Decume, an Aes Sedai of the Age of Legends.
It is speculated that Egwene al'Vere may be the reborn soul of Latra Posae. Indeed, Egwene's role and interaction with Rand al'Thor (Lews Therin reborn) immediately prior to the Last Battle closely mirror those of Latra's prior to the Dark One's imprisonment and Breaking of the World. Egwene initially rejected Rand's proposal to break the seals on the Dark One's prison and formed a large faction of Aes Sedai and world leaders to oppose him. However, unlike her ancient predecessor, Egwene is convinced to aid in Rand's plan and the female Aes Sedai and Rand's followers are able to amass a joint assault on the forces of the Dark One which eventually leads to a decisive victory of the Light.
Canonical proof, no.
As far as I've been able to find, including by searching interviews with Robert Jordan and Brandon Sanderson, none of these theories, or any other theories on Egwene's past lives, have ever been canonically confirmed one way or the other. We're stuck with speculation, I'm afraid.