If you want to shoot it, here's the best way I've found. Remove the old flaking finish, and get some Watco Wood Rejuvenating Oil. Warm it and slather it on the bow. Let it soak in for a day, then repeat at 24 hour intervals for a couple more days. Then brace the bow with a long string-maybe 4-6" brace height. Let it sit a day. Increase the brace a few more inches, and sit a day. I apply more oil each day just to try to fill every single cell I can reach. I do it again at 12", 15" ,20", and 24"(tillering stick). I don't leave it braced overnight at 15, 20, and 24, just for a few minutes. If it makes it through 24", then just crank up and draw it all the way. Either it's gonna shoot, or you can stir paint with what's left of it! Seriously, I did it on a lot of dried out old lemonwood and hickory bows, and only lost maybe one out of 20. However, you want to be sure the glue joints appear sound, and I would fill any cracks with loctite 420 before starting.
If you just want a wall hanger, apply watco danish oil, french polish, tru-oil, or whatever pleases you.