Wouldn't get along.
Our would feel neutral about eachother at the very least.
A lot of people think they'd be friends?? Probably because of the fact that they share the same role in the game and are both "insane".
However, I don't really feel like this would be the case.
Nagito is like a broken record, repeatedly speaking about hope and despair. He also puts a lot of blind faith into hope and luck.
Kokichi would probably dislike that about him, and might find him boring.