No real reason to use any of that flush stuff IMO...if the radiator is bad, replace it, no question. If you can find someone that will flow and pressure test it for free (some radiator repair shops will) then that would be your absolute best/cheapest bet. How much junk comes out or how it looks from the radiator cap is worthless info.
I'd empty the radiator and at least run clean water through the system a few times, draining and refilling repeatedly if the system efficiency is in question, and you have no intention of replacing it.
If there is silicone visible around the t-stat housing, it's probably been monkeyed with, and is likely bad. If the radiator was the problem, your upper hose would have been hot too....obviously it and the fan is working if the radiator is cold.