Gamfreak is crazy. That's why :>
These Evolutions seem to occur as a byproduct of what the Pokemon are based on. See below.
Dragonair ---> Dragonite
Dragonair to Dragonite is kind of just the transition between two similar types of dragons.
It appears to be based on sea serpents or ryu, traditional Japanese dragons or Chinese dragons who bring good luck.
Dragonite resembles Japanese sea dragons, or European dragons, or fairy dragons; its description as the "guardian of the sea" may also suggest it has elements similar to the Chinese dragon.
Perhaps this could be explained simply by the theory of evolution. I mean like apparently we were apes according to that :I so why can't Sea Serpents become Sea Dragons? :P
Alternatively they're just different kind of dragons. If you look at Chinese Mythology, you have those long elongated dragons with tiny arms and wings. And then you also have those massive, typical dragons with big wings and all that.
Magikarp ---> Gyarados
Magikarp is based on a legend about how carp that leapt over the Dragon Gate would become dragons.
Magikarp = Useless Karp (It's also based on the Asian Carp)
Gyarados = Sea Dragon/Serpant thingy
This could also relate to the fact that Magikarp can climb waterfalls and all that. They leap over waterfalls to become Gyarados :I
Several waterfalls and cataracts in China are believed to be the location of the Dragon Gate
See the relationship between the Dragon Gate and Waterfalls. :D!
Feebas ---> Milotic
It also seems to be based on the classic fairy tale, The Ugly Duckling, where a small and feeble "ugly duckling", treated as an outcast by other animals, blossoms into a beautiful swan.
Feebas is a combination of feeble (weak) and bass. Feebas is also phonetically similar to phoebus (Latin for shining one), possibly alluding to Milotic, its evolved form.
Feebass = ugly fish
Milotic = b00tiful shining fishy thing
Trapinch ---> Vibrava ----> Flygon
This one is the easiest to explain tbh.
These three Pokemon are based on the animal the Antlion.
It is based on the larval stage of the antlion, which live in conical sandy pits before maturing into winged adults.
Vibrava is based on the adult stage of an antlion.
Flygon is based on the winged, adult stage of the antlion, which highly resembles a dragonfly.
So yeah you can see the resembelence. Trapinch is the wingless, larvae form which burrows in the sand. Vibrava and Flygon are the adult, winged forms thus also explaining their typing. The fact that Vibrava and Flygon also seem to draw inspiration from Dragonfiles could also explain their typing.