This is another common one.
You are quite right, the moon has no atmosphere. Therefore, it cannot be a natural breeze, or wind. Let's analyze this in more than one way.
If it was staged then, where would the wind come from on Earth? Outside of course. I would have no idea why anyone would film the moon landing outside on a windy day. If it where inside, I'd have no idea why anyone would have a fan aimed at the flag. Also, it would appear that perhaps the US government was too lazy. It doesn't really add up. Possible though for a conspiracy theory, but unlikely.
This particular conspiracy neglects one thing. The flag. The flag wasn't any ordinary flag, it was specifically designed to stay upright, otherwise it would droop down due to gravity and there wouldn't be much point of that. The flag was more than likely 'blowing in the wind', but the action it took was not caused by wind, rather, astronauts trying to plant the flag on the ground. Remember, the flag will remain in an upright position not a dropped one.
Go and try shove something in the ground. It's better to twist and turn it correct? If you apply some basic laws of motion to that, you would realize that the flag would most certainly wave around, and, because of it's upright position imitate a sequence of events that look similar to wind causing it.