We had our cockatiel "Jolly" long before we got our furkids, she rides on Dounia's (lab) back, she loves Chelsey and talks to her a lot, she calls the dogs for me, but shes not fond of Chanel at all, Chanel tried to nibble at her once, so now when Jolly is out of her cage, i carry Chanel in my frontcarrier so i can watch her lol
 
Just be careful with your furkids and the bird, i think its instinct to hunt them, they will get used to the bird