with flaps lowered your Clmax of the aerofoil increases but your stalling angle decreases.
Correct. Using only
trailing edge devices (flaps) the AoA corresponding to CL max is decreasing. Looking at the old propeller transport aircraft (DC-6, Lockheed Constellation) during approach you can notice the nose down attitude of the aircraft. With zero AoA you are already very close to stall with full flaps. Today Aircraft like the BAe 146 are a good example of aircraft that approach with nose-down attitude due to trailing edge devices only.
Figure 1.33 (page 41) in Decurion´s NASA link illustrates this behavior.
With
leading edge devices (Slats, Droop nose, Krüger flaps...) you increase the AoA corresponding to CL max, hence today you see significant nose-up attitudes of most modern Aircraft when landing.