Col,
this is strange, I have never seen a nut on the pin of an air flap. Or is it a bolt glued into the flap during a repair? These pins on original flaps have no threads - see photo.
In any case you need to loosen the angle bracket with the plastic bushing to remove the flap. However the nut you see holding the bracket is welded and cannot be removed. The screw needs to be removed from inside the cabin as shown in the photo (grabbed from Ulli at Pagodentreff.de). There is also one for the other flap inside the cabin.
BTW, do you have a RHD car? I am asking because you show the flap on the driver side of a LHD car.