Angle of attack is defined as the angle between the relative wind and a line from leading edge to trailing edge. What else could it be? Ailerons and flaps move the trailing edge, so their main function is to change the AoA of the wing section. They also increase camber, but that is incidental.
There are two points here -- one is about convention, the other is about the relative magnitude of two effects.
Conventionally, when the effect on a wing section of flap is measured for various AoAs, the AoA is measured by reference to the original chord line. But I agree that you could look at the section with flap deflected as being a new wing section, and that the chord line has changed to accommodate the flap, changing the "effective AoA". That's just a definitional thing. What's more interesting is what proportion of the change in lift comes from the new shape, and what proportion from the new effective AoA, to the extent that it's possible to partition the effects.
If I look at
Abbott and von Doenhoff figure 100 (page 195), it shows experimentally measured lift coefficients for different AoAs and different flap deflections of a 20% chord sealed plain flap for a NACA 66(215)-216 aerofoil.
The plain section, with no flap, has a lift coefficient of 0.2 at zero AoA, 0.92 at 8 degrees, and maximum of 1.42 at 16 degrees.
Deflecting a flap 15 deg gives a lift coefficient of 0.85 at zero AoA, 1.4 at 8 degrees, and maximum of 1.75 at 15 degrees, where those AoAs are measured in the conventional way with respect to the original chord line of the section.
Looking at the effective AoA, dropping a 20% flap by 15 deg lowers the trailing edge by an amount equivalent to about 3 degree tilt of the chord line. So you could argue that those numbers are 0.85 at 3 deg "effective AoA", 1.4 at 11 degrees, and maximum of 1.75 at 18 degrees, where those "effective AoAs" are measured with respect to the new chord line of the section with the flap deflected.
You can compare those numbers with the effect of changing the AoA of the entire original unflapped section by 3 degrees. At 3 degrees the lift coefficient is 0.5. So one could roughly apportion the effect on the original unflapped section of extending 15 degrees flap at zero AoA as being 0.3 from tilting the original chord line, and 0.35 from changing the shape (camber) of the section.
That's actually more to do with the "tilt" than I had suspected, and more to do with the "camber" than you had suspected.