No, that is way to high. It should be somewhere around 180-190 while cruising. Towing or climbing a lot of hills, maybe somewhere around 200-205.
Something is wrong. It could be a bad thermostat, bad impellor on the water pump, of your radiator is clogged internally or externally. Look for a lot of leaves and debris between the radiator and A/C condenser first. Then look at the thermostat.
Flushing the radiator at that time wouldn't be a horrible idea. It would be better if you could remove the radiator so you and hold it upside down and flush it with a hose from the lower nipple with a garden hose. Maybe you'll be able to knock some debris loose if the radiator is partially clogged.
As far as the water pump, the only way to know for sure on that is to remove it so you can see if the impellor has separated from the shaft or if the impeller has been erroded away.