Flaps donīt REALLY decrease the max AOA - they reduce the angle the pilot can play with.
Just remeber the basic definition of an AOA; the angle between the relative wind and the chord line (chord line being a STRAIGHT line connecting the leading- and trailing edge of the wing). So basically the AOA increases immediately when you put the flaps down because a new chord line is born i.e. one from the leading edge of the wing to the trailing edge of the FLAP that now is lower than when in was buried in the wing. So you already have increased the angle "between the relative wind and the chord line" somewhat by lowering the flaps, so it follows theat you, as a pilot, are left with a smaller angle to play with (less upward pitch) before you hit the max AOA.
Taylor