The phrase 'a fish out of water' certainly didn't come from flying fish. These ocean dwellers swim very fast (around 59 kph) which allows them to leap out of the sea. Thanks to their rather large pectoral fins and rigid bodies, they then glide through the air. By whipping their long tails through the water whilst gliding, they can stay airborne for up to 400 meters.
It's no wonder that in 1917 poet Charles Wharton Stork (1881 - 1971) chose to capture them in his poem An Ode to Flying Fish: