Yes, you can loop flag videos, though it's not an exact frame-to-frame loop.
Watch a few seconds of a flag animation with a constant wind speed and you'll see areas where the motion is close to matching. Use a short dissolve to help the transition between your flag movies. Replicate to get the length you need. I seem to recall Zax posting a more precise explanation here a while back. If I can find it in the archives, I'll post it in this thread.