This is an old one that's rumbled on for years. It's another of these irritating conspiracy theories that some people seem to have an impulsive desire to propagate. It ranks alongside crop circles, the Diana conspiracy, UFOs, aliens living amongst us, JFK and the 'grassy knoll' etc. What all these theories make a point of doing is ignoring the simplest and most logical explanation - which is usually the truth.
The flag has often been shown to have moved under its own momentum in the vacuum of space as well as in the blast of the LEM's exhaust when it left the lunar surface. The shadows of the LEM were brightened by background reflection from the lunar surface.
I think Neil Armstrong's reply couldn't really be bettered when this theory was put to him years ago. He shrugged his shoulders and simply said " Well, I know I went to the Moon".