Is hand flapping/kicking legs and hitting out when over-excited normal for an adult without autistic spectrum disorder?

NO: Obviously this is not "normal" behavior for any adult. There may be other psychiatric issues causing this but autistic spectrum disorder seems the most likely cause by far. Kids on the autistic spectrum tend to turn into adults on the spectrum, though often symptoms can become less severe over time, especially with proper treatment, which can include dietary changes, supplements and homeopathy.