No, you don't need a radiator flush.
But, running straight water won't cause a bike to overheat / overflow. Sounds like you have another problem.
I'd start by pulling the radiator off and cleaning the fins really good. Just remember, don't use high pressure (like from a pressure washer) as it can bend fins. also if you have a bunch a bent fins use a comb and straighten them out.
Next check and or replace the thermostat.
If that doesn't do it you have bigger problems.