Can hand flapping be a symptom of anything besides autism?

Yes: And, the diagnosis of autism is not made by a child only having the hand flapping movements. Two other main characteristics seen in children with autism are problems with both communications and social development. I would seek an evaluation with either a child psychiatrist, a pediatric neurologist or a developmental pediatrician.

Just flapping: Not all children with "stereotypies, "repetitive motor movements that seem to have no function, have autism. A two-year old who hand-flaps when excited, but has normal social communication and no other signs of autism. May be developing typically. Less commonly, stereotypies persist into school-age. Tics and compulsions can look like stereotypies. Video it for your pediatrician to check it out.