Fair catch or not
 

I'm fairly new to the site, so I apologize if this has already been discussed.

R1 is in position to receive a scrimmage kick. R1 gives a valid fair catch signal immediately after the ball is punted, drops his hands, then as the ball gets closer to being caught waves both hands above his head, thus an invalid fair catch signal. The ball was caught, we threw no flag and the game went on without incident. Should there have been a flag?

Yes. Even though he game a valid one first, he later gave an invalid one, and thus a flag should be on the ground.

Welcome aboard! Hope do see you more.