I coated a haddock filet in flour and then fried it in olive oil. I let it reach 120 degrees Fahrenheit. When I went to flip it it fell apart and broke into sections. What do I need to do to cook a fish so that it binds together? What chemical processes cause this to happen? Why did my fish not bind?
Your fish didn't "bind" because cooking fish actually breaks down the muscle fibres. Some fish have denser flesh that holds up better to frying and grilling. Tuna and swordfish are two common examples. Other fish have a flakier flesh such as haddock and red snapper.
Haddock is a good fish for deep frying. You can also bake it to have it maintain its form. If you wish to fry it you need something thicker than a coating of flour to help it hold together. You can coat it in batter or do a flour/egg wash/corn meal coating. If you really want just a flour coating you should probably start by cutting the fillets in half.
In terms of equipment and technique you should have a wide fish spatula and, with the fish lying lengthwise across the pan, you flip the fish away from you. You can even stabilize it with your fingers as it rolls over.
Alternatively, you could pan fry a fish more suited to the application.