I envy professional cooks who have mastered the technique of flipping an omelet with a quick motion of their wrist. I am a home cook, so my methods are not as impressive. One way to flip the omelette is to use two wide spatulas. But this sometimes results in the omelet getting torn. Another way to do it, the one I demonstrate in the video below, is to place a heatproof plate on top of the skillet, then invert the omelet into the plate, and then slide it back onto the skillet, cooked side up.