As Tim Wescott said a ways back: "They make the pattern prettier, but I don't think it's just the judges. They keep the fuselage tangent to the line of travel of the airplane, unlike a flapless stunter that needs to point nose-in on corners." (and in round maneuvers like figure 8s as well!)
I, too, believe that fact is one of the primary advantages of any sort of trailing edge flap on a stunt ship. The ship's fuselage profile looks better, particularly in intersections of round eights, clovers, etc. Put another way, the fuselage is more likely to align itself with the path the aircraft following"
I do not believe, however, that massive amounts of additional lift from flaps is "the" secret to the performance of excellent, high scoring patterns with tight corners. I'm a 15 to 20% of wing chord flap advocate like Frank.
(Definition pertinent to what follows: An adverse pitching moment in this case is defined as a lift force produced by the "shape" of an airfoil such as when a flap is deflected on a "symmetrical" airfoil thus modifying it into a "cambered/lifting" airfoil. When flaps are deflected "down" the wing will "pitch" nose down unless countervailing force such as more powerful pitch devices i.e. an aft stab/elevator, forward "canard" surface is deployed to overcome the pitching moment OR if the CG of the vehicle is aft of where the lift resulting from the flap deflection is centered. Early combat flying wings and Bill Netzeband's Fierce Arrow stunter and Half Fast combat ship are examples of "flaps" being utilized as "elevators" via the pitching moment they created.)
A "flap" factor I do believe is important is that the adverse pitching moment wingflaps produce when deflected allows us to utilize CGs well aft of where we could fly with accuracy with an unflapped stunter. The "control load" produced by that adverse pitching moment provides a force "against which the pilot must work during maneuvers which provides "feel" to the input that would not be there were the CG located in the same place (near the center of lift ~25% MAC) without flaps. IOW, an unflapped airplane (given a large enough tail for stability at a 25%MAC CG) would provide feel only resulting from the deflection of the elevators...a comparatively minor source and such an airplane would feel very skitterish to the pilot and precise manuevers would be very problematic)
It is also of interest that the unflapped stunt ships we're used to also provides "feel" to the pilot with the CG forward in the 15% MAC or so which is where the CG usually ends up after flight trimming. That "feel" is also the result of adverse pitching moment by the way...in this case the result of the CG being forward of where the lift to support the vehicle is centered thus increasing the necessary elevator deflection to achieve the desired pitch rate. Ergo, the pilot gets a feeling of more input effort required to do "tricks" and that feeling provides a tactile sense to properly flown tricks, i.e. you can feel what you're causing the ship to do. that additional "sense" of performance is missing if the CG and the lift are in the same place on the MAC.
One of the beauties of modern control systems is our ability to adjust ratios/neutrals, etc. to refine the airplane's trim to optimum. Where response is prompt but controllable and uniform in both directions. Again, flap chord should be in the "modest range" of 15 to 20% of the chord at any point and deflection relative to the elevators adjusted to provide adequate lift for the pattern the pilot is comfortable with plus a modest amount more to account for adverse conditions when the occasional need to insure abrupt inputs to "save the day" don't result in stalls at inappropriate altitudes...the third corner of triangles, for instance.
An example of that last was my original Trivial Pursuit which flew competitively at many Nats over its years of service. It was never a light weight tipping the scales at close to 70 oz on 650 or so square inches and was flown for a long time with one to one flap/elevator ratios. Place second at its first Nats powered by a VF .40 and flew very crisp corners. At a much later hot and humid nats it displayed a scary stall in the third corner of triangles. The ultimate fix for this problem was an increase in flap deflection for a given elevator deflection. I could detect no significant difference in response but the stall issue never resurfaced.
Sorry, too much as usual. Bottom line is I'm not a big flap, big wing, max possible lift advocate. I think the flaps are much more important for refining the appearance of the tricks we do...for much the same reasons Tim addressed.