only the pokémon that does the last hit to faint a wild pokémon earns the exp. set the rest of your team to defend or false swipe so they do not poach kills as you try to train your karp.
magikarp is also in the slow levelling group, and as such suffers from the slow group exp bug - it will have been caught with a total exp too low for its currently level, needing a few levels' worth of exp to level up for the first time; until its total exp reaches where it should be for its first level the blue exp will not display correctly.
so either it is earning exp and you aren't noticing (open the profile and check the numerical exp total), or it is not fainting any wild pokémon from which to earn exp (open the profile and check the earned EVs - if it has fainted nothing, it will have 0).
magikarp is also in the slow levelling group, and as such suffers from the slow group exp bug - it will have been caught with a total exp too low for its currently level, needing a few levels' worth of exp to level up for the first time; until its total exp reaches where it should be for its first level the blue exp will not display correctly.
so either it is earning exp and you aren't noticing (open the profile and check the numerical exp total), or it is not fainting any wild pokémon from which to earn exp (open the profile and check the earned EVs - if it has fainted nothing, it will have 0).