The caption to the pic below says "The slot makes the flat wing act like a proper airfoil. Simple."
How about a slat on both sides of a sheet wing? Simple?
I don't know about "proper airfoil" but a very neat way to make a slat that works in both directions is to put a flat sheet in front of the LE, hinge it from a frame on the front, and put stops to prevent it from moving more than about 30 degrees either way. Just let it float free - when you need positive lift, it flop up, and creates a slot to channel the air over the top, and when inverted, the opposite. Where you put the stops, and whether you want to let it free-float or put a spring on it, is an interesting experiment. The same principle could be used to create a drooped leading edge with a little more work.
I have seen an airplane with the free-floating slot/flap in front of the wing LE. The problem appeared that it worked far too well, and far too abruptly, at least with a conventional airfoil. Of course, you could create a variable slot/drooped LE that was driven by the controls, too. That, I haven't seen aside from some thought experiments I did.
I very strongly suspect that anything you can do with slots/slats/flaps and a flat-plate wing would be better solved with a built-up wing and a conventional airfoil, but it would still be interesting to see.
Brett