As others have said, blinking is not the same as flinching, as the former is a reaction to an event that has just occurred (well, you could blink in anticipation, but I consider that an eye flinch), while the latter is done in anticipation of the same event, and is far worse because it can throw off your aim. Blinking is not so bad as long as it's quick and doesn't interfere with your aim or speed for the next shot; when you reach a high level of skill, however, it may start to become an issue.
Interestingly the two can be related to one another in an odd way, at least for some people, such as me. When I first started out, I had no discernible flinching issue (slow-fire only), although I did blink after every shot. As I trained more and more, and harder and harder, I found it increasingly difficult not to flinch every few shots. This might seem ironic, but basically the faster pace of shooting was starting to get to me in some way, which was frustrating because I had expected to become more accustomed to shooting, not less! So what I started doing--and I'm not exactly sure how I did it--was force myself not to blink so that I could better monitor whether and how I would flinch.
Once I could see everything at all times, including the effect my trigger pull was having on my sight picture, I very quickly became a lot more comfortable with defensive shooting in general, my flinching problem practically went away by itself through visual feedback and practice, and I became progressively faster at recovering and shooting followup shots. I don't know how many people would benefit in this way, but not blinking sure helped me make the most of my training and improve more rapidly.
By the way, I'd be lying if I claimed that I never flinch or blink now, although I rarely do anymore.
I've seen the flash from my 357, and I've wondered if the flash alone would make you blink. Kind of like someone hitting you in the face with a flashlight. Blinding bright light = blink?
Sometimes if it's really bright and your surroundings are dark, sure. Frankly, I don't like either flash or blast in defensive situations, and I take this into consideration when choosing defensive weapons and loads, although I suppose that I should do some adverse-condition training (right now I'm still working to improve my skills).