Perfectly normal operation. The cooling system has numerous sensors that will cause the fan to run for a few to 10 minutes or so after shut down when triggered.
Make sure that the cooling stack is clear of debris and watch your coolant and oil temps. If they fluctuate abnormally you could be dealing with a thermostat, sensor or MAF sensor failure. I suspect that you'll find everything to be within normal operating levels and that the fan is just ridding the engine bay of some excess hot air. Chances are that you'd be getting a CEL if any of those systems were failing.
Rad flush will probably not make any difference but, if you are past the 3 year mark since the last flush, it is recommended in the maintenance schedule and certainly won't hurt.
Best regards
Ross