First, your egg should not be too fresh. I mention this in case you happen to have your own chickens or buy eggs straight from the farmer. Otherwise ignore it.

Second, your pan needs to be super nonstick. I have a small cast iron pan that is used only for frying eggs in butter. Never anything else. And it was used once or more a day every weekday for years - my youngest especially liked to head off to school "on an egg" as they used to say in the UK. It is truly well seasoned. Usually before I flip the egg, I give the pan a bit of a shake to confirm the egg moves around. If it's stuck, when you trip to flip you will rip it. If so, move the flipper around under the egg to free it before attempting any kind of lifting. Remove the flipper and shake again to make sure it's free.

Third, and probably most important, the thing you're flipping with needs to be thin and smooth. A lot of things they sell to flip eggs with really suck. It also needs to be wider than the yolk by a good amount. Most of the plastc utensils for non stick pans are too thick and also not very slippery. Mine is metal but the pan doesn't mind, and it doesn't have those slots cut in it that so many slices (UK) or flippers (US) do.

Then you need the confidence to get in there and flip it all in one motion, not mess about pushing it around and suspending it in midair for too long. The yolk breaks when you lift up half the egg while the other half is stuck to the pan, when you lift it in a way that has a weight of white hanging down on either side pulling at the yolk, or when you put it in at an angle. Practice is part of it, but practice with the right tools is key. When my ideal flipper was dirty, I used to use different ones. I stopped when I realized I broke the yolk with substitute flippers quite often, and never with my preferred one. So I take a moment to wash the flipper if I need to.