Flat covering - my favorite (lol). I can never seem to find enough space or time to do it well!
I'd say the covering depends on how much travelling your flats will be doing, what treatment you're using on top of the canvas, etc. I guess the usual is probably a medium weight canvas ... I usually get it from Rosebrand, which has offices in both LA and NYC -
www.rosebrand.com. They have a lot of helpful info on their website. If your flats are going to see a lot of abuse, I'd consider building studio flats and fronting them with lauan, but they'll be a lot heavier.
Good luck!
LiLz