Antifreeze turns brown after running the vehicle

There are two types of coolant flushes - chemical and water. The chemical flush is much more thorough than the water flushing. Most of the time flushing with water consists of draining the system and running water from a hose through it for a couple of minutes and then refilling it. That won't get all the rust and grime out of the system.When you add the new coolant, the cleaning agents in it are then doing their job and removing more rust and grime. That is one of the functions of radiator fluid, as it contains rust inhibitors and cleaners in addition to anti-freeze. I'd try to do another flush, with a chemical cleaning agent which you can get at any auto parts store. Dump it in and run the vehicle for a while, drain the system and repeat, then give it a final flush and refill, be sure to use the exact recommended coolant for your vehicle too.