In the AC Climate Control system are small electric motors - the flap is probably operated by a motor or pnuematics. Sounds like a worm drive or gear not quite engaging. Some flaps are motor driven and linked by arms. Dirt in the motor/arm/joints can result in slow movement/resistance/vibration. The noise could also be generated by air passing a thin flap - bit of plastic liner sticking out into the air stream.
Try different main fan speeds. Watch the different flaps. Use a video cam or microphone up close to the flap/source of the noise.