The fan is supposed to kick on when it's idling so it draws air across the radiator and won't shut off even after you kill the motor until the temperature switch says it's below the limit. It's working the way it's supposed to. I would recommend you check the expansion tank level to make sure it's above MIN when cold and if you want to make sure the system is operating at the correct pressure a new radiator pressure cap may not hurt. Somewhere in these threads I've posted all the thermodynamic theory on the cooling system of the Gen 1 Rockets and you're free to browse those threads to see if any of the issues raised apply to your particular situation.
So, if you're seeing a difference post ant-flush in cooling behavior there are several possibilities, I'd start with the pressure cap replacement to ensure you aren't boiling off the coolant (water). It's a 50/50 mix of antifreeze and water and the water can be boiled out of it leaving only antifreeze which is a very poor coolant. Antifreeze is awesome in preventing the cooling system from freezing in winter but has very poor specific heat capacity in BTU's per pound mass. The cooling medium is the water which has extremely high specific heat capacity, about 1190 BTU's per pound mass at atmospheric pressure so water is your friend in the cooling system. The pressure cap makes sure the boiling point is raised above 212F so the coolant remains subcooled so the water pump doesn't have to pump a water/steam mix. So, after checking your expansion tank if that's still good then the pressure cap is the next thing. After that it's look at the radiator cooling fin channels, are they blocked so air doesn't cross a significant portion. After that it gets expensive as the water pump is the next thing that could be the problem. It's basically a rabbit hole we'll chase down, but I like to start with the easy stuff first.