It does not weather very well in the wash. The fold starts to become thread bare in a matter of months if it is washed on a regular basis.
At a very minimum if you really, really want flannel, I would back it with Bosal 100% cotton stabilizer. Then, you also want to be sure to sew it at 1/2" rather than the standard 1/4" and cut on the bias to give it added durability (Cut on bias at 2 5/8").
I can't make any recommendations about doing self-binding. I've tried it & it just seems much, much more difficult & time consuming than a basic double-fold French binding. The only reason I'd ever do that again is if I didn't have enough material to do a standard binding.