I wouldn't use foam. I've experimented with foam mouth plates before, and while they do give the mouth flexiblity, they don't retain their shape very well.
Like Slackbot said, gasket rubber is probably your best bet. Just remember not leave at least half an inch, if not more, of space for the hinge, and when you're fabricating the puppet not to pull the fabric too tight, otherwise you'll end up with a puppet with a permanent smirk/sneer.