So far there is only Flying Press.
The reason being that a move having 2 types has potential to be broken (inb4 16x weakness when Ludicolo uses sig.move on Geodude), and Flying+Fighting just happens to have no shared SE-match-ups, not requiring any polishing.

There is tons of already existing moves that just as much deserve being dual type. If the gimmick was properly taken care of, we could have those. So how do we do that?
-Making weakness-modifier cap at 4x?
-make the secondary type only half as strong?
-calculate both match-ups, halve them and add together?
-???

Examples of potential moves:
-Fire Punch, Heat Crash (Fighting/Fire)
-Thunderpunch (Fighting/Electric)
-Ice Punch (Fighting/Ice)
-Bug Bite (Bug/Dark)
-Earth Power (Ground/Fire)
-Muddy Water (Water/Ground)
-Leaf Storm, Leaf Tornado (Grass/Flying)
-Blizzard (Ice/Flying)
-Steel Wing (Steel/Flying)
-Solarbeam (Grass/Fire)
-Petal Dance (Grass/Fairy)
-Ice Burn (Ice/Fire), Freeze Shock (Ice/Electric)
-Scald (Water/Fire)
-Bullet Punch (Steel/Fighting)
-Magnet Bomb (Steel/Electric)
-Psycho Cut (Psychic/Fighting)
-Twinneedle (Bug/Poison)
-Sludge Wave (Poison/Water)
-Megahorn (Bug/Fighting)
-Fire Fang (Fire/Dark)
-Thunderfang (Electric/Dark)
-Ice Fang (Ice/Dark)
-Poison Fang (Poison/Dark)
-Dark Pulse (Dark/Ghost)
-Drill Run (Ground/Steel)
-Shadow Punch (Ghost/Fighting)
-Flame Charge (Fire/Electric)
-Aura Sphere (Fighting/Psychic)
-Dragonbreath (Dragon/Fire)
-Ominous Wind (Ghost/Flying)
-Signalbeam (Bug/Electric)
-Water Pulse (Water/Psychic)
-Poison Jab (Poison/Fighting)
-Hydro Cannon (Water/Steel)
-X-Scissor (Bug/Steel)
-Beat Up (Dark/Fighting)
-Ancientpower (Rock/Psychic)
-Razor Shell (Water/Fighting)
-Mystical Fire (Fire/Psychic)
-Water Shuriken (Water/Dark)

-plenty of signature legendary moves using the Pokemons type combo (Spacial Rend, Fusion Bolt, Luster Purge, Dragon Ascent, Oblivion Wing etc)

how is this not a thing?

>would be too confusingggg
fuck off, you're the reason for masudas smartphone bullshit