Lightly butter a 10-inch skillet, heat over medium flame/coil, add an egg and break the yolk. Once fried, practice flipping the egg using only the skillet in hand and a semicircular motion of the arm. Repeat.
Repeat.
Repeat again.
Repeat until he has it down.
Once he can flip an egg without an utensil, he can make incredible omelets.
Whip three eggs together in a prep bowl with a fork. Add the eggs to the already hot and greased/buttered/oiled pan. As soon as the eggs start to solidify, take a spatula and push the egg an inch or two towards the center while tiling the pan to allow uncooked egg to run from the top to the uncovered pan. Rotate 90 degrees and do the same. By the time he’s gone around the pan once, all of the liquid should be cooked to at least a gelatinous consistency.
Use the spat to ensure that no part of the mass is sticking, and then flip it as described above (I flip over the sink, even after 20 years of experience. It can still go wrong.)
Quickly add the already prepped omelet ingredients (cheese both first and last, if included) to half the egg bed. Use the spat to lift the half without ingredients over the other half, creating a half-moon in the pan. Then either flip from the pan to the plate, of flip with spat in pan and slide onto plate.
Unlike the meager stuffed scrambled eggs that most restaurants call omelets, he’ll end up with an airy and fluffy egg jacket a quarter-inch thick around his well-chosen ingredients. It’ll fill half a plate, and satiate most comers. It’s dead simple, satisfying, and impressive to see done.
Get good enough, and one can even cook eggs over easy with the flip.
I’ll tackle just about anything in the kitchen nowadays, and it all started with the egg flip I was taught in a small-town diner. A learned skill that builds confidence and produces an impressive result leads to a lot more confidence, skill, and willingness.
ETA: And per the OP, no real cooking skill involved. Cut and prep the omelet fillings, whip the eggs, and you’re good to go. Just master the flip.