Flaps increase the "angle of attack" on that portion of the wing that has flaps.

Higher "AOA" generates more lift

The truely great thing is that the inboard section now has a much higher AOA than the outboard. It is like super washout.

And check out the flaps on my Bonanza project. Notice they are tapered. Therfore the inboard side of the flaps are at a higher AOA than the outboard end of the flaps. This adds even more washout effect and more stability.