Mike~
I'm a big fan of sealing cork and wood with Spar Varnish prior to priming, but I would not bother with burlaped birds. Instead, I would prime with flat oils. I typically do this in approximations of the final tones. I use Flat White, Flat Black and Flat Brown from Rustoleum. I can mix the approximate tones with these 3. Then, I topcoat with latex house paint.
What species are you doing?
All the best,
SJS