The chord line is the AVERAGE of the camber of the wing. By deploying a split flap, you are changing the angle between the Fuselage and the chordline by changing the camber of the wing.
For a given attitude, this WILL increase A of A.
Split-flap DOES change the curvature (camber) of the wing- Look at a picture of an aerofoil with and without split flap deployed- when they are out, the wing has (on average0 greater curve.