I don't think you can completely "flush out" the old coolant without a shop or special machine. But by simply draining the radiator and refilling it once a year or every 30k miles should keep the fluid cycling and fresh enough that you shouldn't have to do a complete flush...
[then there's all the other issues with complete flushes that involve removing helpful deposits, causing premature leakage, $$$...]
Ted Kazinsk... er... Unabombers Coolant FAQ
Scooby Mods Rear Differential Fluid Change
Scooby Mods Transmission Fluid Change
[FWIW, i've got Mobil 1 Synthetic 75w-90 in the Rear Diff and NEO Synthetics HD 75w-90 in Transmission] [fluid doesn't solve shifting problems, proper shifting solves shifting problems, and if it doesn't, your transmission has problems...]