When I was first diagnosed with arthritis I was treated with Plaquenil. It was back in the early 90s and I don't recall Fibromyalgia being something thrown around all that much; however, it wouldn't have surprised me that Fibro was part of my illnesses.
Anyways, Plaquenil did nothing for me. I took it until it started causing problems with my eyes. The doctors figured I would have felt some great increase in pain but I didn't. They were surprised that it really wasn't working for me, even though I had told them that many times. They insisted it was a great drug and figured it was at least doing something.
However, different drugs work differently on different people. I'm all for giving something a try if it's going to help my quality of life. I'm not interested in living until 90 if my quality of life remains the same.
Anyways, they use Plaquenil for many auto-immune disease so I see no reason why it wouldn't be tried for Fibromyalgia.