Hi my almost 6 year old has been arm/hand flapping all her life only when excited or proud. If she draws a picture and is showing it to me, she will flap her arms, rub her fingers together, and open her mouth in excitement.
When she was an infant her whole body would shake/tense when excited. She doesn not match any of the criteria for autism but her other traits are she has had extreme social anxiety and had been selectively mute for 3 years but is coming out of it with the help of 5 mg of paxil. She no longer is selectively mute and is making friends easily now.
Her flapping actually got worse for some time (in frequency and duration - 10 seconds instead of 4 seconds) about 3 weeks after we started her on her paxil and she started standing on her head any chance she could get (because it "feels good"). Then suddenly the flapping stopped for about 2 weeks and now is starting up again. She had normal development during childhood, aquired language early, smiled, great imaginary play, walked at 13 months. She has had an issue with tantrums but now we are realizing it was probably related to her anxiety and has decrease dramatically since the meds. Have you seen this type of flapping in non-autistic children? If interested, I can send you a video of her flapping but I don't want to post her on the internet so I'd send it to you privately.