What fish can blink its eyes?

A shark is the only fish that can blink.

General consensus is that the shark (most -- not all types) is the only fish that blinks, however:

Sharks don't blink in the way that we are used to. They have upper and lower eyelids, but these lids don't move and don't close over the eye. When biting prey, some sharks protect their eyes with a third eyelid called the nictitating membrane.

https://en.wikipedia.org/wiki/Shark

Not all sharks can "blink."

Fish in general, do not have any kind of an eyelid, or nictitating membrane.
http://www.seafriends.org.nz/photolib/eyes.htm

Not all sharks have eye protection called nictitating membranes. Of the 453 shark species worldwide, there are about 15 species that lack this eye protection.

Some species in New England coastal waters without a nictitating membrane are: the white, shortfin mako, porbeagle, thresher, sand tiger, dogfish, and basking shark.

http://newenglandsharks.com/Page1whatisashark.html