Gluten-intolerance is a big component of Hashimoto's ... wheat may be causing your bloty as well. Tale L-glutamine powder (5 grams per day) to help keep enterocytes in better shape. This also raises glutathione (GSH) levels, and GSH is the major liver cell protection enzyme. (precaution, don't take L-glutamine if pregnant. It is unstudied.)
fluconazole is a VERY strong antifungal. Doctor should prescribe also pills to protect the patient's liver (e.g. http://en.wikipedia.org/wiki/Silibinin)
I just wanted to clarify my question. Did your doctor have a reason for thinking that you have a yeast overgrowth in your gut as opposed to something else? Chronic stomach bloating is usually something else besides yeast overgrowth, so I was wondering if you had eliminated other more likely possibilities or had some other symptoms that indicated that this was yeast overgrowth as opposed to something else.
As far as I know, the only way to test for candida is a really expensive DNA stool test, or when you have so much overgrowth you can see the spores in the stool samples.
If it is candida, the fluconazole is safe. It is not killing probiotic cultures in your bowels. And 6 weeks is not really longterm, especially since fluconazole is not an antibiotic, but an antifungal. Candida is a mean one, and hard to get rid of. But Candida hates a balanced diet with lots of beans, veggies, wholemeal, yoghurt and fruits. Reduce your meat and sugar intake to aid the meds to kill it off. Good luck!
Welcome to the gastroenterology community! Did your doctor do any tests to come to the conclusion that you have a yeast overgrowth in your gut?