[thejacobhartman]

first off, why, you should not need to unless you have replaced a part due to contamination or have inadvertently contaminated it yourself.
second flushing the system is a pain without a large reservoir to hold incoming fluid, 2-3 gallons of fresh fluid. other wise you risk burnig up your pump.
the easist way to do it at home with the motor off is to disconnect the lowest point and drain it then reconnect and fill. then run it around the block four or five times. then do it all again a couple of timeswith fresh fluid each time, making sure to top off before leaving the drive way