And on the other side of the coin, chickens that are nervous and act it will trigger normally good dogs. So getting both the dogs and chickens comfortable with each other is really helpful. It's the same with dogs and cats. Cats that are confident and will stand up to dogs generally don't get chased. My dogs are great with confident cats and will even sleep and cuddle with them, but as soon as the same cat runs for any reason, the dog is after them because it's just their instinct.I would introduce on leash to prevent chasing and see how things go. Your birds will likely bolt if the dogs act as though they'll chase and that's what you often need to curtail. The desire to chase prey.
I would be most concerned with the collie but the Chihuahua could also feel that desire.
I have a fence, one yard for dogs and one for chickens.