I really don't know what in the world is going on with her but when I think food allergies, I think itchy ears and paws. That doesn't mean it is not that, but my first thought would be mites. That is the kind of itching it sounds like (crazy and uncontrollable) and the armpits would go along with that.
So I'd either do a skin scraping (you might even need two if the first one is negative) or possibly just treat for mites anyway (without a positive scraping).
If that doesn't work then I would probably think food.
She doesn't have any kind of rash, does she?
Couldn't have gotten into anything before this happened?
The Italian dressing could've gotten into the middle of the chicken somehow but it is surprising that a little bit of something they had never had before would cause such a severe reaction (unless they have eaten those any of the ingredients before).
As for washing the flossies in diluted bleach water, are you sure you want to do that? Unless you soak them for a long time the middles aren't really going to get cleaned well and that just seems so toxic to me. I just give Ellie raw vegetables.
By the way, if it is mites and both vets never thought to test for it, I think I would be upset. I think mites are more active at night, so she could have incresed itching then. Also, I think warm/hot water stirs them up and starts the itching.