Is it best to put heatercore back in F-150 before flushing radiator
If it is a new heater core, you cannot put it back in to the vehicle before flushing the radiator. This is because it is possible for clogging to occur in the coolant system if not flushed. You should charge the coolant regularly.
Put it back in but if it's a new one flush first in install
Flush your radiator before reinstalling the heater core. You don't want the gunk in the radiator to clog up your new heatercore.