I did my sons car like this. Removed the lower radiator hoses from radiator. Removed the thermostat housing and kept it attached to the hose. Used a hose nozzle wrapped in a rag and inserted it into the intake where the thermostat sits. Ran water for several minutes. Reversed the flow by shooting the water through the lower hose so it came out the intake. Once it ran crystal clear I disconnected the heater hoses. Used a small nozzle and flushed the heater core and hoses going both directions. I then rinsed out the radiator same method, both directions, until crystal clear. put the lower hose back on the rad and added 1 gallon of 100% coolant. Then added 50/50 mix until it flowed out of intake. Installed new thermostat and closed it all up. Topped it off and bleed it out. Good to go
Don
this works well, but if you put the lower hose back on, leave the T stat out and the upper hose on the housing, and off the rad. put the hose in the rad, fill it up, then start the car, run it till clear water comes out the upper hose, then turn the hose off, then run the car till no water comes out the upper hose. turn it off. then put the T stat back, the upper hose back, then dump one gallon of straight antifreeze in the rad, start the car full the rest of the way with hose water.
then idle the car rad cap off till the fans turn on, then bleed the air out of the t stat housing, top off the rad as needed as it warms up, if it burps and the rad level drops, the T stat opened up for a a few seconds and took the coolant, the cold water from the rad made it close again.
waiting for the fans to come on means its hot enough that the T stat should be wide open.
you can also pull the heater core hoses off the back of the engine, and flush it both ways with a garden hose. then put the hoses back on, but fill the hoses with water so no air gets trapped in the core.