Last car I cleaned out, we attached the hose alternately to either the radiator drain plug or the expansion tank overflow pipe into the rad, dropped three tabs down the top hose, ran the engine until the temp gauge hit 100, then simply popped the cap off. Once the resulting volcano has calmed down, skim the gunge from the header tank and repeat... twenty times
The rapid expansion of the water in the sytstem helps blow the muck out, and by alternating opposite corners of the rad, that ensures it gets flushed too
To add, when the hose is connected to the drain plug, the hose from the expansion tank to the radiator is removed from the radiator and diverted to a bucket.
When the hose is connected to this pipe, the drain plug is closed
Edited for clarity