Here is a video of me flushing out my heater core...here are the symptoms to make me do this:

Heater had very little heat, even when the car was up to temperature, verified by the dash gauge and laptop reader. Temperature into the heater core was super hot, but water returning from the core was only kinda hot...aka not much flow so most of the heat was being removed from the water.

Repair:
To take the heater core system and wash it out with clear water, insert a "cleaning" product to dissolve any gunk that didn't get rinsed out, and then rinse that out. Return it to service. If the buildup in the core isn't too bad, this should boost flow through the heater core.

Result? It worked. A few bigger pieces of stuff came out during the initial rinse and some rusty colored water came out after the cleaning solution. The heat out of the heater core at idle is very hot, so flow has appeared to have been restored.