I can hear the water gurgling in heater core inside the car, but the heat comes and goes.
It's a new heater core from last winter. This is a 99 Taurus and I had a 92 that did the same thing. How do I get all that gunk out of there to unstop it?

See if you have a faulty heater control valve or problems with the controls thereto.

A Taurus does not come equipped with a heater control valve.