Egg binding can cause a temporary paralysis of the legs, because of pressure on the sciatic nerves in the legs. I have never witnessed it, but it can happen. Botulism can occur from eating the botulinum toxin produced in dead animals and vegetation after being buried without oxygen. The reason I don’t think that you are dealing with that is that botulism is not a mild illness. It causes first, paralysis of both feet, then legs, then wings, and neck followed by the eyelids in less than 12 hours. It is more of a problem in waterfowl, but it can occur in chickens. There is no treatment this far along, but if treated early an Epsom salts flush can be used. That can dehydrate a chicken, so at this point, it really wouldn’t help. The 3 possible problems seem like either riboflavin deficiency, temporary egg binding paralysis, or hopefully not, Mareks disease. But I am not a vet, just giving an opinion.