The short answer is a wet slippery deer hide. Which when it dries is going to be very stiff. If I recall correctly, it has to stay immersed for a couple of weeks, and when it comes out, the hide has to be worked. Stretched flat or pulled, then neatsfoot oil rubbed into the flesh side. Do your homework, because I'm working on a half-memory and one cup of morning coffee.
Everys animals brain contains enough tannins to tan their hide.
What's the best way of getting the brain out for such a use?