Installing a slate floor over existing vinyl floor?

Are you sure its just over plywood and not luan? If there is luan underneath, it could eventually delaminate and cause the floor to fail. Otherwise, you're fine going over vinyl, just use a belt sander to rough it up. Also, if youre going to self level, do it over the backerboard, just make sure to use a latex primer so the SLC adheres to the backerboard.