I think someone else already responded with the idea of using bone buttons. Should be sewn out of braintan. If you can afford it or make it yourself. If you ever use modern tanned hides be sure to soak them and pre-stretch them before making your clothes. This item was brought west with the pony soldier's uniform.
Most sewing today is done with artificial sinew.
Someone mentioned linen thread. If you're not going for the real sinew then either the artificial sinew or waxed linen work great. Linen has the advantage that it won't stretch and eventually tear as easily as the art. Eagle Feather, Crazy Crow, and Grey Owl all carry both. I also used to think they were common.