I don't flap my hands either. But I have noticed that I often will hold my right hand up near my chest (think T-Rex, lol).
I crack my knuckles and play with my hands, just moving them around while my fingers are intertwined.
I play with (squeeze/pinch) my mouth/lips, chin, ears, neck, pick my eyelashes. My wife calls me Nicker Picker (my name is Nick).
Echolalia, I usually mouth or whisper words rather than say them out loud.
Make quiet clicking noises with my mouth/throat. When I was younger I used to make much louder (non verbal) noises of various sorts but I learned to mask that until they are no longer one of my natural stims.
Move my jaw forward and backward.
Very lightly tap and grind my teeth
Whip pencils and pens back and forth. Especially love Pentel Clic Erasers with the eraser sticking out 3/4 of the way
Move my shoulders around, forward, back, up, down, popping my back behind my shoulder blades
When swinging my arms while walking I'll brush my fingerprints against my outer thighs
Scrunch my toes, tap my toes
Tap my fingertips on just about everything
Blink my eyes (not sure if this is because of dry eyes or a stim. Probably both)
I love fidget spinners (especially with the nicely firm poppets built in), flippy chains, "Hacky Sacks" (to squish and squeeze), the afore mentioned Pentel Clic Eraser, the feel of writing with a pencil or a fountain pen