Um, I hate to sound like I'm defending your neighbor, but long before I owned chickens I'd been through flooding in the middle of town when nobody even near me had any kind of animals, and my yard still smelled like a broken sewer. Wet chicken poo has a very strong ammonia odor. Is that what you're smelling? Or could it be the flooding quite literally did cause a broken sewer pipe or backed up storm drain and it ended up on or near your property?
In either event, Diva's advice is spot on, as usual. As a former city official I can tell you that they can't fix what they don't know. I'd call them out, either the sanitation department or the town maintenance crew, and let them make the final determination as to the cause of the odor, and knowing your area better than we do they'd be the ones to advise you on cleanup without putting your health at risk.
Again, I'm not defending your neighbor if his sanitation left something to be desired. But having been through flooding where no animals were present, I can tell you that either scenario is possible. Oh, and good luck! This can be a real wooley booger to get resolved.