wtf
I can't believe the number of red herrings here:
Spanwise lift distribution and elipsis.. full span flaps still work (see some gliders), so no (secondary effect).
aspect ratio.. plenty of types have flaps that do not vary the aspect ratio, so no, secondary at best
I'm pretty sure we covered it in the first 2 replies:
1) Flaps change the *camber* of the wing. That changes the lift / drag curve for the wing
2) Generally, flaps increase the lift at the penalty of increased (total) drag. At a given lift that will translate to a reduction in required AOA.
If for some circumstance the more cambered wing section, at a lesser AOA produces less *induced* (not total) drag than the flatter wing section at a higher AOA, the original posters scenario is complete. Right at the stall would seem a likely candidate, but it's simply a matter of comparing L/d curves.
However, the induced component of drag would seem slightly irrelevant, as it's rather impossible to separate from total (induced + parasite) in practical terms.