Aviendha's visions of the future show the fall of the White Tower. Aviendha's line is as follows

Aviendha
Padra
Oncala
Ladalin *
Tava
Norlesh
Malidra

It is during Ladalin's lifetime that the White Tower falls. Ladalin cannot channel, and she is an old woman. Her fingers are "knotted with age". So it is late in the third generation of humanity after the LB. Each generation is probably 20-25 years apart, so we can infer that the WT falls about 100-120 years after TG.

Even with the Three Oaths, all of our favorite channelers who survive Tarmon Gaidon (and presumably don't die from something else) will still be alive, especially we consider how powerful channelers are who were born about, oh, 25 years before TG. How powerful you are determines your lifespan, and since Cadsuane was over 300 and she's weaker than the Wondergirls, they would probably live at least 350 years. Presumably, this means a middle-aged Egwene, the Amyrlin, will become damane again, or die.

I find that this makes me almost as sad as the fate of the Aiel, in and of itself. As silly as most Aes Sedai can be from time to time, the White Tower really is a monument to the strength of humanity. If everyone who can channel is kept in chains, I don't see how humanity could ever return to a different state. Obviously it worked in Seanchan for 1,175 years (according to timelines, I'll link below). For the sake of fair comparison:

Seanchan empire has existed, complete, for 1,175 years.
The Breaking was about 3,000 years ago.

If they take over the known world, it will be a long, dark time for everyone.

Somehow, I feel the most sorry for Egwene.