it is my humble opinion that there really is no natural substance that will 'cure' or be of great benefit to Hashimoto's Thyroiditis, although I could be wrong.
Most people who have Hashi's benefit from suppressing the thyroid by taking prescription medicine in certain dosages.
Armour natural thyroid works the best (imho), and is not expensive, even if you don't have insurance. If you can't afford it, there are programs for low-income people -- your doctor can sign you up, if you have a doctor who will prescribe Armour, that is. A Naturopathic doctor can deal w/ this issue far more effectively anyway. You can also purchase it online in various places.
Iodine, which is the component that makes people take kelp supplements for thyroid conditions, can seriously aggravate Hashi's.