A Group of Flamingos Is a Flamboyance

The proper collective noun for flamingos is a flamboyance.
English has a long tradition of colorful group names, known as terms of venery. Flamingos are a rare case where the name matches the animal almost too well. Their pink comes from pigments in the shrimp and algae they eat.
Check it yourself
Look up collective nouns for birds at a major zoo or bird conservation site. The pigment story is on many zoo pages too.