I disagree that once an aquatic creature leaves the water it will accelerate further. Think about it. The critter pops out into the air, where it has no means of creating traction for movement. It isn't going to accelerate at all, only lose speed. I am not an engineer, but this seems obvious to me.

it's cool that a fish can fly that far out of water!!! but i think that it's wrong people blame the animals and other creatures for doing the killing... They say like in this one "DEATH BY FLYING FISH" if you think about it it's not the fishes fault it was the fact that the person was in the wrong place at the wrong time!!! Don't get me wrong I would be mad at the fish to if it killed one of my loved ones... but for the most part the fish had the absolute right to swim there... it's not his fault... you could have been swimming over his home... we do so many horrible things to animals, yet we blame everything on them... we are smarter than the animals isn't it time we took responsibility for what happens to us, ourselves???

No, that's incorrect. Fish will break the surface with the front part of their body and skate along the surface briefly with their tails still in the water, generating thrust, like a ski boat up "on plane." (If you imagine that same ski boat motor on a submarine, it wouldn't propel it nearly as fast.) Once top planing speed is reached, they adjust the angle of their fins to launch themselves upward.

They move faster in air than in water. Less resistance. Only gravity pulls them back down, slows them down.

Fish can keep moving faster, once they are moving faster. But the question the OP had, which I answered, and you and the author ignored or didn't understand, was how they got moving faster than their underwater speed in the first place.

It's the instantaneous acceleration due to a change of medium. Think of it this way, the sum of forces will equal the mass times acceleration. The sum of forces includes a positive force (which causes the fish to move forward) and a negative force due to friction of the water. When the fish leaves the water, it encounters less friction and there is an increased motive force. This is translated to an increased acceleration. It's the same idea of skidding something across a rough surface and then transitioning to a smooth surface. Right at the moment you make the transition, the object will speed up greatly if you don't change how hard you are pulling on the rope.