Not all of these work for a duck-flamingo pair but they might for some similar configurations:

Bird Brains with Heart

All Hands On Duck
(That one might invite rude behavior, I fear)

Flamingo Liberals

Par Avian

Ornithological Orneries

Fowled Out

(High) Pop Fowls

Fowl Mouths Speak From The Heart

Eider One Orni Otter (but you'd need a mammal along for the ride)

Let Osprey

Crazy As A Loon

Peeking Ducks

Bird Floozies

Duck and Cover

No Quacks, Please

Flying The Coop

Fine Feathered Friends

Mocking Birds (We sure are!)