YouTube - Apollo 15 waving flag
If you look at the size of the astronauts' arms when they are near the flag and look at the size of the astronaut's arm when he goes by the flag, you'll see it is quite larger when he goes by the flag. He is probably three or four feet from it. He couldn't have touched it.
If you double-click quickly on the mouse to make it go frame by frame, it's pretty clear that he doesn't touch the flag.