It's a good idea, but if you choose a wimpy fabric, the fibers can stretch, then the hinge gets shifty. the pros use 3mm kevlar cloth laid at a 45 degree bias. It kind of ruins the simpleness to your idea, though. If you make the gap really tight, with the flap side of the joint beveled, then maybe a continuous strip of Tyvek would be the way to go? I would use the thinnest amount of epoxy and lots of pressure to make this part. might even sand a faint relief in the wood to account for the thickness of the fabric strip.