It does not sound as though he is displaying two of the three diagnosis criteria for Pervasive Developmental Disorders - delays in social interaction skills or communication skills that cannot be attributed to another organic disorder (like cerebral palsy) – so I would not be overly concerned with pursuing a diagnosis of autism solely based on the fact that he engages in stereotypy ( the hand flapping you described).
Stereotypic behavior (simple repetitive movements like body rocking, hand flapping, non-functional vocalizations) is a fairly common problem that is seen in both individuals with developmental disorders and in typically- developing infants and children. Research shows that this behavior is typically occurring as a form of self-stimulation (rather than a way to access attention or other events), and that it is not harmful so long as it is not interfering with skill acquisition or producing some type of risk. If the stereotypy is interfering with his learning, you might try some simple interventions to reduce the stereotypy: if he is supposed to be working, redirect him back to the task; when stereotypy does occur, prompt him to place his hands on the table or his lap; finally, try finding some toys that have stronger sensory properties (vibrating toys, etc.) and allowing him time to play with those. Because stereotypy is such a common problem, I wouldn’t worry that it has deeper implications or pursue further diagnoses.
Regardless of his diagnosis, childhood behavior problems like stereotypy can typically be addressed through consultation with a Board-Certified Behavior Analyst (BCBA). If you feel that the behavior is stigmatizing or interfering with more adaptive behaviors and the simple interventions I noted above haven’t been effective, you may want to consult with a BCBA. The school district may have a behavior analyst on staff that can provide some recommendations, or you can contact a local BCBA at the following site: http://www.bacb.com/consum_frame.html.
Many children on the spectrum do hand flap. One of them is my 6 year old. However, you may want to look into Sensory Processing Disorder first. The behavior you described is sensory based. If he doesn't show the social aspects of autism I'd start there. Making an appointment with your local OT is a great place to start. Make sure they have experience with pediactric/sensory. If not it is worth your time to go to the closest one who does. Hope that helps you.