What is the best way to completely flush the radiator and whole system?

The best way to flush the system is to drain the system and remove the thermostat, then refill the system with water and the flush chemical and drive it for a day. Then drain the system again including the block plugs (these can be difficult to remove). What I like to do is refill the system with water drive it for a day then flush it out again and keep doing this until you are happy with the clarity, then drain the system one more time and refill with straight coolant. There will be enough water in the block to give you the correct dilution.

This guide can help:

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

Please let us know if you need anything else to get the problem fixed.