If you really want to run anti-freeze into/thru the tank flush system - here's an idea (although I haven't tried it yet).
First, some assumptions:
You have a threaded connection on the flush system
You have an external shower/hose with garden hose connectors on it
You have a winterizing bypass system
Take a gallon container of anti-freeze. Put the winterizing system dip tube in it (so far, just like winterizing any camper). Put system in bypass mode.
Connect your external shower/hose to the tank flush connector.
Start your water pump, open the cold water valve on the external shower. You should now be pumping pink stuff throughout the plumbing system, including through the external shower and into the tank flush system.