That works, I also use 2 slatted frames. However, the mattress comes over the edge of the bed and then tends to slide back and forth because it is no longer held in position by the frame. The slatted frame supplied is relatively flat.
Yes, you'd better use the slats supplied with the bed frame. A normal mattress already sticks out quite a bit. With unsuitable slats, it would be even higher and the mattress could slip.