I can totally relate to you. My son does this and is now 6 years old. He was diagnosed with autism at 3. I don't really know if he will outgrow this, though. I've been told soooo many things; some have told me that they eventually will; others have told me that in order for a child to stop doing that, he/she must have sensory integration therapy. But, as you know, every child is different, be they special needs or not.
My daughter flapped when she was small (until about 5). It's a form of self-stimulation. If your son does stop flapping, he will likely start doing something else to replace it. My daughter stopped flapping and started twisting her fingers. Now she paces when she can't jump or skip.
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