You piece is probably not mounted in wax as you suspect. The stones are likely ''glued'' into the setting, and the glue is just old, this is a method often used in costume jewelry and a way you are able to tell precious stones from non-precious.
They would not glue a diamond or otherwise precious stone into a setting. Diamonds will almost always be firmly set. The flaking you describe is characteristic & consistent with machine made stones & settings.
Sometimes they will pull the gold up onto the back of a precious stone to keep it in place, but it would not flake away as you describe. I hope this helps.