It isn't a behavioral problem. It's instinct!!! Dogs are carnivores and, as such, almost all dogs have a relatively high prey drive. Because of this, almost ALL dogs will try to attack a prey animal flapping around helplessly. There is a natural urge for them to attack the lesser animal in the flock, and this is why you need to physically separate your birds and dogs.

I NEVER EVER EVER let my birds loose in a room with Giselle or Lucky. Even if they are muzzled, they can still grab the tails of the birds, knock the bird's head against the floor, and essentially kill the bird. To prevent accidental deaths, cage your birds whenever your dog is in the room. If you want to let your birds loose, lock the dogs out and be sure you are in the room to supervise the bird anyways. Birds left unsupervised in an empty room are dangers to themselves. Good Luck and I'm sorry for your loss.