Before you proceed with any actual repairs it is important to inspect your air vents thoroughly for any damage such as cracks or loose parts. Inspecting this will help in understanding the actual damage and the reason for the air vent whistling.
If you find any loose bolts and screws in the vent and secure the connection as loose bolts between the ductwork and the blower fan are the ones causing an excess amount of noise. These parts will click as the air blows or you can hear a whistling as the air passes through the gaps where the bolts are not secure.
After checking and securing the loose connection you should start inspecting each of the inner parts of the car air vent starting with the blower motor. The motor circulates the air inside the vent allowing it to cool your car.
If you don’t find any issues with the blower motor you’ll continue checking for any leaks and cracks around the air vent. If you find any holes chances are that air is passing through them as the vent circulates air thus causing the whistling noise.
In some of the car models you’ll find a cabin air filter inside the vent, it will remove the pollen dust and any dust that enters the car via the air sometimes this filter can get clogged and cause air vent whistle whenever the vent is on.