There are two times when the average individual remembers that Gyarados is also a flying-type pokemon: On New Years, when inflatable Gyarados floats are carried through the air (real Gyarados having an unfortunate tendency to get bored and attack the crowd), and in elite pokemon battles, when they remember their vulnerability to stealth rock and stone edge. This is not strange, for although they do not touch the ground outside of the water, they move at low altitudes and seem as though they are gliding through the air.
In reality, a Gyarados' four pairs of wings make it a superior flier to most birds. They are known to leap out of the water and match Wingull for altitude, flapping their wings until they catch and devour them. Some even pose a danger to small, low-flying aircraft, for Gyarados are ferocious and are known to break windows to get at human prey; aviators and historians alike are all too aware that the first three attempted transpacific flights ended this way.
It is commonly believed that, because a Gyarados's slippery scales and awkward, twisting flight motions make them unsuitable for carrying human riders, they are overlooked among flying pokemon. I am less convinced, for my observations have given to me a far more likely explanation: that humans, to keep a primal terror at bay, avoid contemplating and even remembering the fact that Gyardos can fly.