How do you prevent salmon from falling apart when frying?
The best technique I've found for frying fish is not to flip it at all. I start the fish on the stove, skin down, then I finish cooking it in the oven. You need an oven safe frying pan of course, cast iron or a high-temperature non-stick works well. You get a nice crispy skin this way. 

If you are set on flipping then you need to be gentle, think of it as turning over, not flipping. Get your spatula completely under the fish and lift it off the pan a bit, then putting your fingers on top of the piece roll it over, last let it gently drop onto the pan - keeping your fingers off the surface of course.