Mosquitos can travel indefinitely if caught in a storm (and not killed for some reason or other). Females can become dormant and survive for 6 months in that state.
But plenty of Pacific Islands didn't have them until recently, Hawaii is much closer to a continent than most of them. The Pacific is almost all volcanic Islands that rose from the sea. So it's not a common occurrence.
The problem is not so much how far they can disperse, but how far they can disperse and breed. A pregnant female only lives a few days. Males only live about a week. So even if a female makes it to an Island, quite possibly it won't find anything to eat in time. Or it lay it'sits eggs, but they don't find anything to feed on.