Like CamMom, I relate to this very strongly from my own experience. If I were a child these days, I would be identified as "stimming" and sent for evaluation, I'm sure. I used to rock forward and back (sitting or standing) when looking at something that strongly interested me, or when thinking about exciting ideas that did not require a visual reference (I had many elaborate fantasy scenarios) I would pace in circles with my hands behind me and fingers waving stiffly. I also did a lot of twisting my hair, rubbing my feet back and forth on the carpet, rubbing the ends of my hair against my face, pressing each fingernail in turn in certain specific ways, manipulating beads in my necklace or buttons on my shirt, stuff like that.
I remember as early as preK having other kids comment on this behavior, not so much teasing as asking why I was doing that. Gradually I began to realize it was unusual and to feel more self-conscious. Through elementary school I made efforts to stop the most obvious behaviors when I was in public, and I found that it helped to set up time to do them at home to "get it out of my system"; for example, I would come home from school and take my parents' address book into my room and rock over it playing number games, and then the next day that would help me resist rocking over my math book and--a side effect, but a very helpful one--resist playing those number games instead of listening to the teacher! I also took dance lessons for years and thus learned some moves that "look like I'm doing something" instead of looking weird.
With the smaller fidgeting behaviors with my hair and such, my parents worked hard against the destructive ones (nail biting, etc.) and my best friend had a nice tactful way of mentioning to me in private that something she had seen me doing during school was unattractive. Gradually I became more conscious of what I was doing and more willing to keep my hands under the desk doing something safe and unobtrusive to substitute for other fidgeting.
As late as 13 years old, I remember spending the early mornings in summer pacing on our driveway thinking. But it was a very quiet street; if anyone came outside, I would try to act like I was doing something "useful" such as weeding the flowerbed or practicing my dancing, until I felt unobserved again.
I've always thought of it as a way of channeling excess mental energy so my brain doesn't explode.
As an adult, I still need some of this kind of thing, but I feel I've done pretty well at integrating it so I appear normal. Most days I French-braid the front part of my hair so that I have a long braid hanging down the back of my head, and the loose hair at the end of it forms a spiral curl (I wonder why? The rest of my hair is not so curly!); I can stroke my braid or wrap the curl around my finger while I'm thinking, and it doesn't look too weird--but I avoid doing a lot of that in front of people; it's mostly for fidgeting while I'm working alone in my office. At home I allow myself several hours a week of staring at interesting things while standing up kind of vaguely doing stretching exercises and kind of rocking--I don't need to do it in as structured a way as I did when I was little. I also tend to "wander" around the room, basically pacing, while talking with my partner in the evenings. If several days go by when I can't do these things, I begin to feel very antsy and frustrated.
I used to talk to myself, as well, and gradually learned not to do that when anyone could hear.
I guess what I'd suggest for your son is that you mention occasionally, gently, that his arm-flapping looks a bit odd and maybe he could turn it into something else, for example an arm-flapping exercise like jumping jacks or "windmill" toe-touches. Nobody is surprised to see a person exercising in his yard. Talking to himself is trickier; if there are ever times when you are confused about whether or not he's talking to you, certainly mention that, but otherwise I think you'll just have to let him gradually understand the social awkwardness of talking to oneself--or you could put a Bluetooth headset on him.
I went to a very geeky university where I met a lot of people who clearly had stimming habits they'd channeled in acceptable directions. All of us were interested in a pair of identical twin men who seemed to spend most of their free time walking in circles around a certain tree on campus talking to each other. They eventually were interviewed by the campus newspaper and said this was a game "kind of like Dungeons & Dragons" that they'd been playing together since they were little, discussing and developing their fantasy characters. A lot of us were jealous of them after that. Imagine having another person who shares your inner world and gives you just enough social support that you can indulge in public!
Anyway, I think you are correct in not making a big deal of this but wanting to help him avoid ridicule. It's a fine line to walk. I think my parents did pretty well in addressing only the harmful activities directly and accepting most of my odd behaviors as personal habits. My dad took a home movie of my full-blown rocking and finger-wiggling when I was 4, and I'm glad he did because it was so weird and it's striking to see myself from the outside, but he never ever spoke of it like, "Check out this weird thing Becca used to do!" It was more like, "She was really interested in that Sears catalog!" said in a warm voice, like he found it charming and he really loves me as an individual with all my idiosyncrasies. Just recently I found a reprint of a 1927 Sears catalog at a used-book sale, and when I mentioned it to my dad, he said, "Oh, that'll be good for hours of rocking!"