Some notes on flushing. This is just how I do it.
First, I drain the system as completely as possible.
I have a Prestone flushing tee installed in one of my heater hoses.
Remove thermostat so it doesn't unterfere with flow. Put t-stat housing back in place.
Connect garden hose to the flushing tee. Leave radiator cap off. Run engine with garden hose flowing. Flush 10-15 minutes. Water coming out of radiator should look pretty clean.
Stop engine. Disconnect hose. Drain everything again through radiator drain and bottom hose removed.
While draining, disconnect heater hoses from heater core. Hold the garden hose in the heater core pipes and flush it. Do this in both directions. I then use compressed air ir the "blow" side of my shop vac to try to blow the heater core as dry as possible. Reconnect hoses. Many of us connect the hoses in the opposite direction each time we do a system flush.
Remove the overflow reservoir, empty and flush clean. You may even be able to get a bottle brush inside and clean residue off the tank walls. Empty, dry, reinstall.
Install thermostat with new gasket. Reinstall lower radiador hose and close drain.
I then pour concentrated antifreeze into the radiator to equal about half the system volume. Start adding distilled water. While adding distilled water, I start the engine to circulate everything. At this time, I have the radiator cap off and the cap is still off the flushing tee, which is at the highest point of the sysyem to let air out.
When the coolant starts bubbling out of the flushing tee, I cap it. When radiator is full, I put its cap back on.
Fill reservoir with 50-50 mix or pure coolant.
Stop engine and let it all cool off. As it cools, it may draw coolant from the reservoir. Top off as needed.
Check frequently over the next few days of driving and top off the reservoir if needed.
In my mind, this gets me the most thorough flush possible. Some engines have a block drain plug to help get the block drained good. I've never messed with that on my engines. But it would add a small degree of efficiency in getting old coolant or flushing water out of the block.