Flapping , sensory issues, picky eating, and obsession are all behaviors commonly associated with autism. It is possible to make good eye contact and also be on the spectrum.
My DD was not diagnosed until age 11, and a substantial part of that was because she always had good eye contact. It is totally possible to be autistic and capable of good eye contact.
If you're being told by people who don't actually work with autistic kids that he doesn't show signs of autism, I would pursue getting him evaluated by an actual autism center. The worst case scenario is that they don't diagnose him with autism and you're in the same place, right? But if they do, trust me that you want to know about it now and not when he's 12 and running away from school personnel and making them worry he's going to be hit by a bus.
