Generally you cannot fully flush the system without special VAG tools/diagnostics due to various one way valves etc.
My DIY fix was to drop the main (bottom) radiator hose and get as much out as possible. It was actually done at the same time as a cam belt/water pump change so worked out well. That was 4 years ago and so far so good.
You could drop the hose, fill up, drive a bit and repeat. It's not that scientific though. Do you drive a TDI? The blocked heater matrix is a well discussed topic.