I flapped in a very conspicuous classic autistic manner, holding my hands fairly high and agitating them so that it was a visual stim as well. During my first years at school, this attracted great attention and intrigue, including from adults and high school students, and was deemed unacceptable by teachers. My unpleasant third grade teacher was particularly intent on stopping this, but she didn't succeed. My fourth and fifth grade teachers only gently reminded me that I was flapping. I'm quite sure that I was no longer flapping in seventh grade, and am not sure about sixth grade.
Considering the sometimes humiliating efforts undertaken to get me stop, I wouldn't say that I outgrew the flapping, as much as I was forced to give it up. In a way, teachers were right in getting me to stop because the type of flapping I did would have been a major embarrassment in later years. I can still flap exactly like I used to, but I haven't done it involuntarily since those early days.