Some Pokémon are bred. Some are trained. And some are simply waiting for a home.
Baby K. is a special baby Kangaskhan available on Cobbletwo through an adoption system. This is not a reward, not a prize, and not a farmable mechanic. It is a one time opportunity to give a young Pokémon a place in your team. You can adopt it at the daycare farm by interacting with it.
At the farm, you will also notice that there are other baby Pokémon around the daycare. They are part of the place, part of the atmosphere, and part of the story. They wander, play, and make the farm feel alive, but they are not available for adoption like Baby K.
Baby K is the only one that can be adopted, and only once per player.