This fabulous footage from the BBC series 'Life' shows some wonderful slow motion footage of these spectacular fish.  The predator shown in the clip is a Sailfish.

Flyingfishes come in two 'kinds', the four-wing flyingfishes (like those in the movie) have both the pectoral and pelvic fins enlarged. The two-wing flyingfishes have enlarged pectoral fins only. The four-wing flyingfishes can usually glide farther than the two-wing flyingfishes.

Flyingfishes are often seen taxiing just above the water surface, rapidly beating the water with the large lower lobe of the caudal fin.