I built a lot of RC airplanes, but we used some stuff called Monokote, which is a shrink wrap plastic kind of stuff. The old canvas-and-dope airplane coverings are kinda vintage, if you know what I mean.
I would agree that any kind of paint
you use would likely flake off and crack at the stress points. Lets face it, paint
is not designed to be that flexible. If it were me, I would experiment with some small pieces of sail material and dyes. See if I could get crisp edges, not fade out, etc.
Are sails coated to prevent them from absorbing water and getting heavy?
I have also been using iron on patch material made to fix canvas tents and bimini's to repair
a kite board sail lately, and it's working pretty well. Its a sticky light woven material with heat activated adhesive.