Any AoA sensor installed on the wing itself just gives you a "value" that somehow relates to AoA (and is good enough to predict stall precisely), but does not really give you an useful angle information. You need to mount it on a boom at the aircraft nose for accurate measurement, and this is exactly what you would do on a test aircraft.
However, to explain the issue a little simpler, if you deflect a trailing edge device at a given AoA, the stagnation point on the leading edge will move backwards (more circulation required to "bend" the airstream to follow the trailing edge angle, which also heavily affects airflow in the nose region). This means an increased upwash at the sensor.
Additionally keeping overall lift constant (equal to weight) with flaps extended means a higher relative portion of the lift is produced by the flapped inner wing, and less lift is produced on the unflapped outer wing. This increases the wash (upwash ahead, downwash behind) on the inner wing, hence the AoA you are reading.