Flunkey is a feisty, ill-behaved Bandar-log that served as King Louie's servant in The Jungle Book. Despite his kinetic nature, he speaks with a prim and distinguished British accent in the original film.
Obviously, don't nominate any human characters. Hybrids like Cheetah or The Lizard are okay, as are shapeshifters with one set animal form (eg Professor McGonagall.)
