What is the best way to flush out coolant?

I would drain the coolant out the best you can, then fill the system with water from the garden hose and run it until hot, then drain the system again and repeat. Making sure none of the coolant enters the storm drains. Collect the coolant in buckets and then take them to the auto part store for recycling. Repeat until the fluid is clean then drain and add the correct coolant and top off with distilled water. Here is a guide to help you and I have included the drain for the system in the images below.

https://www.2carpros.com/articles/coolant-flush-and-refill-all-cars

and

https://www.2carpros.com/articles/engine-coolant-59420607

It looks like you will need to drain the system by using the lower radiator hose, no drain plug :/ Check out the images (below). Let us know if you need anything else.

Good information, thank you!

You are welcome, please use 2CarPros anytime we are here to help.

I forgot to mention that they added the green antifreeze to the Dexcool already in the system, will clear water be enough to clean out the resulting sludge formed by the mixing of the two?

They do make a cooling system flush at the auto parts store, I would add that in after the first flush to relay help to clean it out.