How I flushed:
Go to Home Depot and get a gallon of Simple Green. After putting the new radiator in, fill cooling system with a half gallon of simple green, the rest water. Run the engine, get it up to operating temp. Make sure thermostat opens and the solution goes through the block as well as radiator.
Shut down and allow to cool slightly. Carefully remove radiator cap, then lower radiator hose. Allow cooling system to dump out in the grass. Simple green is non toxic. You can try to catch in a bucket but good luck. Reattach lower radiator hose, fill with water and repeat above procedure.
After a water flush, use remaining simple green and water in the cooling system. Get it up to temperature, take it for a short drive, and dump the solution.
Now just use water to fill cooling system, run, and dump until it comes out clear. It took me about 10 flushes. After that, remove the overflow bottle and clean thoroughly. Replace the upper and lower radiator hoses, and thermostat. Refill the cooling system with water and antifreeze mix.
I know this seems like a lot of work, but it's the only way to keep from letting the oil build up in the new radiator and heater cores. It also will cause hoses to swell and that's why I recommend replacing them now and not when it blows leaving you stranded.
As for the transmission, it's a similar process. I changed the fluid and filter about 6 times within 500 miles. The shuttering went away and the fluid got clean again. It was foamy and is now pail pink.. not burned, orange or brown.