Gents, whilst the comments about the noise being created by the mechanism being the culprit for the noise is quite plausable. I would suggest that the noise is airflow disruption. The 146 if I remember correctly was designed with a high lift wing section in order to allow it to operate on short strips and have good climb ability linked with its four engines.
Failing that argument / reason - you can hear the 'banshee' noise from the ground, therefore highly unlikely to be mechanical noise. Also the noise continues after the flaps have stopped travelling.
All that said, first time I travelled on one and the flaps where selected the noise certainly startled me and practicaly gave the lady sat next to me a panic attack. Maybe a passenger warning is in order for any new / nervous passengers.