Gyarados not being a Dragon-type makes sense when you look at the tale that it and Magikarp are inspired by.
Magikarp is based on a legend about how carp that leapt over the Dragon Gate would become dragons.
There's a second part to that tale, where the new dragon was violent and had its dragon status taken away because of it.
Flygon: Bug/Flying/Dragon (I have no idea what a dragonfly has to do with the ground)
Flygon and its kin are not dragonflies, but antlions. Trapinch is based on an antlion nymph, which creates elaborate sand pits that other insects can't escape and it waits at the bottom (hence Arena Trap). That's why the Ground type works, but admittedly only on Trapinch. Antlions mature into winged insects like Vibrava.
Annoying as it is; I can't exactly blame the ones who think the tale of the carp ends where he becomes a Dragon because I have seen countless geniuses in an attempt to summarize the legend exempt the part of the tale where the Carp gets his Dragon status revoked while at the same time believing they are explaining why Gyarados isn't a Dragon type.
Gyarados shouldn't even be Water/Flying/Dragon. The flying type should just go away, because it doesn't make any sense on him.
Butterfree: Bug/Flying/Psychic Tyrannitar: Rock/Dark/Dragon Flygon: Bug/Flying/Dragon (I have no idea what a dragonfly has to do with the ground)
After the carp became a dragon, it lost its dragon status because it became angry. I partially agree with butterfree. Tyrannitar doesn't look draconic at all. It looks like Godzilla, which is more of a dinosaur anyways. Flygons evolutions were ground type.
Jesus promised the end of all wicked people. Odin promised the end of all ice giants. I don't see many ice giants around. - ff12and3rocks