Trying to see the sights and the target behind them when the handgun goes off helps me blink less. My understanding is that I should just on the front sight, but if I am having a temporary flinching problem, trying to widen my focus of vision to see the sights and target seems to help.
I have had the same experience!
I recently listened to a podcast from Steve Anderson, a well-known practical pistol shooting coach (and a pretty good unofficial sports psychologist, too) where he talks about a phenomenon that can occur with a really hard front sight focus. He was discussing the idea of seeing the entire recoil arc of the sights (seeing the front sight lift from the notch, track up, return downward, settle) and its benefits in terms of being able to shoot fast without sacrificing a given level of accuracy. He said that some people can actually struggle because they get so intently focused on the front sight that, as soon as it moves, it is just gone from their vision... which, in turn, makes it a little slower to pick it back up on return.
What Anderson was describing wasn't a flinching issue, per se, but I do think it's related. Sometimes a slight softening/loosening of focus can help open up our awareness of visual data that is available. This is part of why I bolded the phrase "see how much you can see" in my OP. Not "look how hard you can look."