A wink is usually considered to be deliberate, to convey a message that something is a joke or there is some secret to be kept.
Defined in this way, you would expect that it would be slower than a blink in order to make sure that the one you are winking at receives the message. Because of this, a phrase that would mean something very quick would probably tend to favor 'blink' over 'wink'.
"In the blink of an eye" just developed that way. I'd say it rolls of the tongue a little more smoothly, but that is an opinion. There is no logical reason not to say "in the blink of eyes." ;-)