To flatten burl veneers you can wet them with water. Mist them with a spray bottle until they soften enough to flatten without cracking. After wetting them place them between a couple of sheets of blotter paper and press them between two flat boards to dry. If you use epoxy to apply the burl it should "wet out" the veneer enough to bend it for a backstrap. Epoxy will also fill the voids burl often has.
Burls are essentially end grain, so they won't add much strength as a back strap. Using a plain light colored veneer under them can add some strength and add a nice contrasting line between the neck wood and burl.