Yeah, I wouldn't bother tumbling it, too fragile. If you do tumble it only tumble it with other amazonite or other material of the same hardness. If you throw it in a tumbler with a bunch of agate the agate will pulverize it and anything else that's softer. well, that's been my experiance anyway.
But yeah, use the main cleavage plane as your flat base and cab or carve as you like. I've never worked it myself but have looked at a fair amount of rough and finished stones. It would be fun to carve it.