Can Porcelain Floor Tiles Be Layed Over Pre-existing Slate Flooring?

It depends on the underlayment and installation of the slate. If the slate is properly installed on a cement floor you could pour self leveling concrete to smooth the surface, then put the porcelain down with the correct type of mortar for a good floor. If the slate is lain on a wood floor without cement board beneath it and you put fragile porcelain on top, the slate could easily shift, flex, or crack, which would in turn crack, and or loosen the porcelain. If you are unsure of the stability of the current floor it is always best to take it up and pour self level or screw down hardi board.