Frank, I have a good friend who has invented a new style of turkey call. This is a 'slate' type call- but doesn't employ slate. He is quite the accomplished flint knapper. Some of his calls look like a large arrowhead but with one side flat. Other models are shaped like a turkey feather. They are made from stone from all over the world. He has a bank of diamond saws in his workshop for slicing the stone into slabs. Amazingly you can vary the pitch of the call quite a lot by manipulating another stone attached too the call and by choosing where on the call you scratch. They aren't cheap. He also makes a turtle-shell turkey call. That call uses the shell of a box turtle as an amplifier. If you want to look at them they are on artofishi.hypermart.net
If you are looking for a 'slate', I would try to find a local lapidary shop that sells slabbed stone. I have found that almost any stone 1/8" to 1/4" thick will make nice turkey talk. I have a piece of petosky stone that sounds real nice. Take a striker along and test drive a few rocks. You can grind a lot of stone types on a pedestal grinder- just wear good eye protection(face shield) and a respirator............Oh, and another thing, if you happen to call in a nice tom and miss him with yer shootin iron, you can always bonk him with the rock..I mean call, in yer hand.