I still cannot believe that so many autistic children toe-walk. I had never heard of it until I got diagnosed with Asperger's last year. I'm almost 20, and I still toe-walk: completely when I'm barefoot, partially in shoes. I just always thought it was something quirky I did. I never knew that it was a "red flag." It still amazes met that so many other kids do it. I've never met anybody who toe-walks.
I agree with the others that the flapping doesn't say anything by itself. First off, not all individuals on the autism spectrum hand flap. I rarely do. Only when I'm extremely, extremely excited about something. Even then, it's not the "classic" hand flapping. (I mildly shake my hands in front of my face. I didn't even think of it as hand flapping until recently, until I saw it for what it truly was.) Some "classic" autism signs to watch out for in conjunction with the flapping would be:
Lack of eye contact or odd eye contact (intense stare)
Lining up of toys
Extreme upset due to change in routine/insistence on sameness
Lack of interest in people/lack of desire to have social interactions
Obsessive interests (in high-functioning individuals, a key sign is nonstop talking about said obsessive interest)
Excellent rote memory
Echolalia (either immediate, such as repeating your exact words right after you say them, or delayed- repeating movie/TV quotes verbatim, something I do all of the time)
Trouble having a reciprocal, "give-and-take" conversation (in verbal individuals)
Hypersensitivies to certain sensory stimuli
Hope this helped!