Want to use some to back a hackberry bow that has a hinge.

Try a weavers supply house. Maybe a large craft store. Be careful with raw flax because it has very little stretch and can over power your belly and cause more problems.

can you by chance just cover the area that hinged and just fade it out in to the limb a little way?

Yes you can. I've never done it though. I have seen rawhide, sinew or wood patches over hinged areas to support the hinge.

You might be able to get some in a plumbing supplies store, I am pretty sure they use that here to help seal pipes as my plumber gave me a big bunch that im sure is flax and long fibers too.