I did the math once on flaps and turn radii once.
The average plane gets its turn radius reduced around 25% with full flaps.
Some oddities:
The P-51, with its maneuvering flaps, gets only a 19% reduction. Meanwhile, the FW-190, with its split-type flaps, NOT designed for combat maneuvers by any means, gets a 24% reductions
The P-38, with its large Fowler flaps (they move down AND backwards to actually increase wing area, very effective) gets a 26%. Not as much as advantage over plain maneuvering flaps as one would expect, to say nothing of the 190's split flaps.
Relevant to this topic, the Corsair gets 40%
Now, the Corsair was designed to land at ~75 mph on a carrier, so it SHOULD turn tighter than a P-47 or P-51 that was typically landed at 95 mph, but I agree the turn is probably a little too uber.