first you have to know what all the different flap types are like. The regular slotted flaps are used by planes like the F4U Corsair and the P-51 Mustang. These are literally a part of the trailing edge of the wing, and they (for the lack of a better word) bend downwards changing the shape of the wing as Murdr stated. This changes the AoA and causes a higher lift co efficient. This helps out in instantaneous turning and to an extent, in sustained turning. There is a cost in drag, however. Dropping the flaps too much consequently causes a drag-lift co-efficient ratio with waaay too much drag so you end up turning uber slow with your nose pointed up high.
Then the enemy just ends up not necessarily outturning you, but turning FASTER.
The next type of flap is the split flap, which the Tempest, Hurricane and Spitfire uses. For the Spitfire and Hurricane (in real life), the flaps are of dual stages. Up (0 degrees deflection) and down (50 degrees deflection). These flaps don't really change the shape of the wing too much and they seem to be less efficient in raising the lift co-efficient without a higher cost in drag than the slotted flaps, but they do cause speed to drop uber quickly. When i used to fly the Spitfire, i'd use these split flaps as brakes and then quickly flip the plane over in the loop, though the F4U seems much better at that than the Spitfire, what with its speed brakes and all
The last, most complicated and (usually) the heaviest flap system is the Folwer flap, probably named after some awesome dude whose last name was Folwer. Anyway, these flaps are usually like split flaps, but don't just extend downward, but rear-wards as well. They end up giving more wing area with a very small amount of drag. The P-38 is fitted with this as is the Ki-84.
Now, Zlehmann, your La-7 is fitted with the multi-stage split flap, which opens up at around 165 mph methinks. They're useful when in dogfights actually. When at the top of loops and slow, you can drop a notch or two to get you flipping over quickly and hammer on top of your enemy. If you want to cause an overshoot, go right ahead, though i doubt experienced F4U and P-38 pilots can get overshot by an La-7. I also find split flaps useful when im really low on speed, but diving BUT still slow enough to drop flaps. At that instant, i'll drop a notch or two and i can follow an enemy for a few more precious seconds. But hey, you can pretty much run away, come back and HO like most La-7's do lol.
http://www.auf.asn.au/groundschool/umodule4.html#flaps