I'd personally say flinching is innate i.e. it isn't learned, but 'programmed' as such, into your anatomy. Thus I'd say it'd be very hard, if not impossible to try and 'unlearn' how to flinch. Just imagine trying to stop yourself from smiling every time you found something funny or were happy.
That being said however, alot of intelligent people's posts suggested otherwise - so you never know.