I've never heard of fasting having helped anyone with fibro symptoms, and myself would never do it because one thing that definitely makes it worse for most people is not getting enough good quality nutrition.
going gluten-free doesn't help with fibro. If a person is gluten-intolerant, as I am, going gluten free will definitely make a huge difference in how you feel, but won't lessen the fibro symptoms as such, and won't help anything unless you are gluten-intolerant already. As far as I know, the only dietary thing that helps is making sure you eat regularly and nutritiously. And that only helps because without that your body doesn't have the calories and protein it needs to deal with anything, let alone fibro.
I would never advise a person with fibro to fast. Personally I think it's a bad idea. But if you choose to do it let us know how it goes.