P47s can't really turn, and even the magical flaps wouldn't help you. What it can do really well is give the illusion of turning well.
The combination of high wingloading, elevator authority and very good stability allow you to go from 400 to 200 mph with the jerk of the stick. This means that not only will spitfires tend to overshoot you, you'll also quicly place yourself inside their turning circle while yourself making a smaller radius turn (due to the loss of speed). What happens is that the spit will not be able to point at you making him feel that you are out turning it, while in practice he's flying around you and into your guns.
It will be easier to describe with a drawing, but I'l try anyway. Imagine two planes flying around the same circle at the same speed (and same G), suddenly one reduces the speed but keeps the same G load. Now the circles will be one inside the other and not less important - not co-centric. The circle center of the P47 will be displaced backwards. The effect of the displacement is that in order to bring your guns on the spit in front you need to turn less degrees. Or if the spit is doing the chasing, he'll need to turn much more than you to bring guns to bear.
Untill you both are slow...
The other thing P47s do well beside burning E is scissors - especially rolling scissors. Good roll rate at all speeds and slow speeds handeling along a line combine to make it a great scissor machine.
Raanan