Flipping the omelet is a circus act degree of acquired skill, scares me every time.
However:
My favorite is flipping an "egg-over-easy" for a breakfast sammich. When you start, put the egg on one side of the skillet and tip it just a bit to keep the egg next to the skillet side, and in a smaller "puddle".
Then when it has cooked up a little and solidified, give it a little swirl to make sure it is not sticking. It'll circle around the skillet.
Move over above your cutting board.
With the egg closest to you in the skillet, thrust the skillet away from you and then pull it quickly back as the egg hits the other side of the skillet and pops up and flips over.
Quickly move the skillet back away from you and under the egg to catch it. Put it back on the burner.
Probably the second time you do it, once you get the jist of it and tone down your flip, you can just do a gentle "flop-over" and not even break the yolk. I'll do two at a time with small eggs.
Lots of flipping and flopping, but don't flip out (Get the yolk?)
You have chummed me up! I’m going to have lunch!