What makes hippos and flamingos get along so well?

So I have a feeling you may have confused the flamingo with yellow billed Oxpeckers, which eat the parasites on a hippos back. The Oxpecker gets food, a home, and protection from the hippo, and the hippo gets to deal with less parasites, so they relationship benefits them both quite a bit.

If you really did mean flamingos, though, I really don't think they pay each other any mind.

There are birds who help hippos with grooming and dental hygiene by picking hippos teeth and cleaning them. Maybe flamingoes are one of those birds. I always thought smaller bird breeds are the only ones who help hippos with that but I could be mistaken.

They're not competing for the same food or living space. Neither is a predator of the other.

Hippos are not hunters. Flamingoes are no threat to hippos.

They pose no threat to each other, like deer and rabbits.

Not giving a sh it about each other.