The rapid onset of the disease and the symptoms make me think that they could have experienced Botulism. Botulism is poisoning that can occur when a chicken eats a dead animal infected with the organisms that cause Botulism, or comes into contact with it by scratching in an infected area. Botulism causes paralysis, lack of coordination, sudden death, inability to stand, a limp neck, and droopy wings. Botulism also sometimes causes the feathers to easily be pulled out. It generally kills within three days. The treatment for Botulism consists of "flushing" a bird with something that will draw out the poison and get it out of the bird's body quickly. An Epsom salts flush is common, as is a Molasses flush.
It might be something else, but this is what I thought of first. Is there any place that your birds could have scratched around in near a dead animal, or moldy food? Or, could any of their feed have become moldy? Sometimes they can also get Botulisum from wet litter when they scratch around in it.