Flushing the system is OK for getting nasty old coolant out of the system but, it isn't going to clean out your radiator if tubes are plugged up. You usually can't see it by looking in throught the cap either. They usually plug more towards the bottom.
Usually when fan clutches go bad, you can spin the fan freely by hand. Not running of coarse. New ones will turn by hand but have resistance. Not keep spinning.
