At what time?
There's no question that the flag is moving after the astronaut passes. A 3D model of the scene shows that his left arm was close enough to the flag (which was rotated toward the camera) to brush past it. The only question is whether this is the only thing that happens, or if there's also some initial apparent movement due to video artifacts.
Don't forget the unusual color system in use. Until it was phased out with the transition to digital, the United States NTSC scheme transmitted linear combinations of all three primary colors simultaneously over three separate channels. The luminance or Y channel occupied the video baseband and the I and Q color channels were carried on a quadrature-modulated subcarrier, with the Y channel being backwards compatible with a monochrome ("black and white") receiver.
Until digital imaging, generating NTSC required three CRT imaging tubes, one for each primary color, and a prism and color filter scheme to separate the light from the subject. This would have required a much larger, heavier and more power-hungry camera for Apollo, so a sequential color system was used instead. A single imaging tube with a rotating color wheel (blue, green and red in that order) carried the primary color images sequentially over a single channel. This signal was converted to NTSC on the ground and relayed to the networks. Because the primary colors are not sampled at the same time, various artifacts were produced on moving subjects. We could easily be seeing some of them here, particularly on the astronaut as he moves into the scene.
