Dog chews and the like are from heavy beef hides. You will need to thin it down quite a bit or else it will effect the arrow speed...and not in a good way.
A better hide would be deer, antelope, or goat. There is an advertiser in PA named Michael Foltmer out of Colorado that sells both whole rawhides of these critters, but also bow backing strips. A whole Antelope rawhide, shipped from Michael, is less than $45, and you got enough to back 5 bows! If you buy just the strips, I think he charges about $20 plus postage. I've bought a number of these hides from him and they are good quality. Few holes in the hides, well scraped, and thinner than the cardstock you would have business cards printed on!!!