The Flame is an ancient symbol, though its original meaning has been forgotten by present-day people.
In the Age of Legends, the Flame, along with the Dragon's Fang, was part of the ancient symbol of the Aes Sedai. Since the Breaking and the splitting of the Aes Sedai to remove the men, the Flame has taken on another meaning. It is no longer connected with female channelers by the common person, and its origins are lost to common knowledge by the passing of years, but superstition still regards the Flame as a sign of female Aes Sedai.
In the Last Battle Egwene al'Vere, while battling M'Hael, creates a new weave as a direct counter and opposite to balefire—a weave of pure creation as opposed to balefire's pure destruction. She calls it the "Flame of Tar Valon". This "Flame" turns foes it touches to crystals, though it works differently on those who choose the Shadow than on those who do not. Overusing this weave turned the entire field on which Taim and his channelers fought to statues of crystal, and turned Egwene herself into a giant pillar of crystal.