According to Aerodynamics for Naval Aviators,
Chapt. 1 - Basic Aerodynamics - High Lift Devices
"One factor common to the maximum lift condition is the angle of attack and pressure distribution. The maximum lift coefficient of a particular wing configuration is obtained at one angle of attack and one pressure distribution. This fact is sufficient justification for the use of angle of attack indicators and stall warning devices which sense pressure distribution on the wing."
In addition to the above passage, there are two figures in this section that show the CL max of a wing clean and the CL max of a wing with flaps extended being attained at a slightly different angle of attack. The numbers in their example graph and figure are...
Clean: CLmax = 1.5 AOA for CLmax = 20 degrees
Flaps: CLmax = 2.0 AOA for CLmax = 18.5 degrees
With these examples in mind, although it is not specifically addressed, I believe that in addition to lowering stall speed and increasing CL for a given AOA, lowering the flaps will also slightly reduce the critical angle of attack of an airfoil.
In the text above, the author refers to an airfoil "in a particular configuration" stalling at the same AOA and P distribution. The author does not however, specifically address the effect of changing said configuration on CRITICAL AOA.
With all of this in mind, this little reduction in critical AOA is NOT the primary reason why an airplane stalls at a much lower PITCH atttitude with flaps extended versus retracted. The effect of Lift and drag that flaps induce is the primary reason for that.