Does the extension of trailing edge flaps increase or decrease the critical angle of attack?
Both right and both wrong, both over simplifications based on unknown airfoils, and so on. Real aerodynamics is complicated and 3 dimensional.

Flaps usually increase the critical angle of attack a few degrees, but they also increase the effective angle of attack for a given pitch. So the net result is that the pitch of the aircraft will be similar at stall with or without trailing edge flaps, but the true AoA will increase.