Are flying fish born with their wings?

YES!!

Most fishes know as "flying fish" are not achieving true flight. Most of these fish are either jumpers (leaping out of water) or gliders. Although, some fish can achieve true flight. For example the freshwater hatchetfish. These fish can exit the water and they will use their elongated and wing shaped pectoral fins in a flapping motion. They will also use their extremely strong caudal fin to generate thrust and air. If thrust and lift are both present, this is true flight.