I'll jump in on this.
You could probably eliminate the flaps without any major problems. Why do you want to?
My experiences with my RV-4 (Everett Hatch-built O-360A1A, 200 hp, Hartzell prop with F-7666 blades, 1070 lbs, CG in a forward location):
The stock plain flaps decrease stall speed from 55 KIAS clean to 50 KIAS with full flaps. Extending flaps decreases the landing roll, but with the RV-4 that really is not significant. I can get the plane stopped in 500 ft with moderate braking. With flaps up that increases a few hundred feet. You could still operate comfortably from 1000-ft runways with a constant-speed prop.
The two major advantages to extending flaps for landing is a steeper approach, and a landing attitude closer to the stalling angle of attack. All RV-4s, even with the newer long gear legs, are still flying in the 3-point attitude, even with full flaps. Landing with flaps up means you are touching down well below the stalling angle of attack. If you plan a fixed-pitch prop, you will find speed control more difficult on final approach without flaps, necessitating a shallower approach.
I practice no-flap landings periodically. No problem, just a moderately shallower approach and moderately increased landing roll.
With a constant-speed prop I take off with flaps up anyway, so there would be no difference there.
You could design and build fowler flaps if you like, but again why do you want to? The RV-4 has such ridiculously good short-field performance anyway that the expense and effort probably wouldn't be worth the slight improvement. With my RV-4, light weight, solo, cold day, max performance gives a takeoff roll of 150 ft. Max effort landing roll, same conditions, max braking, can be as short as 200 ft. Fowler flaps really wouldn't decrease your distances much below that.