Actually no. There was no breeez as the Moon has no atmosphere. The flag was fixed to a pole and suspended from the horizontal bar to prevent it hanging limp. The action of jamming and twisting the flagpole in the surface of the Moon caused it to flutter, and the lack of any atmosphere and hence air resistance meant the flag kept moving. Only its own weight and inertia would eventually stop it moving after a while.
The other factor conspiracy theorists should consider is just how many people would have to have had knowledge of any faked-landing conspiracy. In almost 50 years none have ever come forward, there have been no death-bed confessions, or leaking of secrets to the then USSR - who would certainly have been yelling from the rooftops if the US landings were faked.