Iodine and a good source of plant derived minerals (including trace minerals) would likely be good starts.  In fact, a good whole foods derived all around nutritional product like IntraMAX might be a very good idea.

Here is a bit more information excerpted from http://www.tbyil.com/Baldness_and_Thinning_Hair.htm

Nutrition and Vitamins for Baldness and Thinning Hair: 

• Hair loss occurs when the diet is inadequate in the B vitamins - especially B6, biotin, inositol and folic acid; and the minerals magnesium, sulfur and zinc. The B vitamins, especially B5 (pantothenic acid and B3 (niacin), are especially important for hair growth.

• Certain essential amino acids are found to control the thinning and thickening of hair in laboratory animals. For example, when rats were fed a diet deficient in magnesium, they lost their hair in bunches. The situation was even more serious with some other B-vitamins. When rats were fed a diet low in biotin or inositol, they became hairless! This nutrient-deficient condition was found to be reversible. When the rats were fed a diet that was rich in B vitamins, it resulted in the complete restoration of hair.

• Heavy intake of vitamin supplements, in some cases, has resulted in stimulating hair growth. Men deficient in vitamin B6 often lose their hair. When they are deficient in folic acid, some men became completely bald! As in case of animals, when normal intake of theses vitamins was restored, the hair also returned in most instances.

• Taking large doses of vitamin A (100,000 IU or more daily) for a long period of time, on the other hand, can trigger hair loss, but stopping the vitamin A will reverse the problem. As in case of deficiencies, often the hair grows back when the cause is corrected.

• Essential fatty acids (flaxseed oil, primrose oil, and salmon oil are good sources) improves hair texture. Prevents dry, brittle hair.

• Raw thymus glandular stimulates immune function and improves functioning capacity of glands.  Dosage: 500 mg daily. Caution: Do not give this supplement to a child.

• B-Vitamins - B vitamins are important for the health and growth of the hair. Foods rich in B vitamins include beans, peas, carrots, cauliflower, soy beans, nutritional yeast, bran, nuts and eggs. Take a vitamin B-complex and supplement it with the following additional B-vitamins for best results.

• Vitamin B3 (niacin) - 50 mg 3 times daily.

• Pantothenic acid (vitamin B5) -100 mg 3 times daily.

• Pyridoxine (vitamin B6) -50 mg 3 times daily.

• Biotin - Biotin is very important for hair health. It is needed for healthy hair and skin, and may even prevent hair loss in some men. Eat plenty of foods high in biotin and/ or take it in supplemental form. Good food sources of biotin include brewer's yeast, brown rice, bulgur, green peas, lentils, oats, soybeans, sunflower seeds, and walnuts. You can also use hair care products containing biotin.  Dosage: 50 mg 3 times daily.

• Inositol - Inositol is vital for hair growth.  Dosage: 100 mg twice daily.

• Vitamin C- Vitamin C aids in improving scalp circulation. It is important to maintain capillaries that carry blood to the follicles.  Dosage: 3,000-10,000 mg daily.

• Vitamin E - Vitamin E increases oxygen uptake, which improves circulation to the scalp. It improves health and growth of hair. Since hair health is tied to the immune health, vitamin E is believed to stimulate hair growth by enhancing the immune function.  Dosage: Start with 400 IU daily and slowly increase to 800-1,000 IU daily.

• Zinc - Zinc stimulates hair growth by enhancing immune function. Dosage: 50-100 mg daily. Do not exceed this amount.

• Other Nutrients That May Help Hair Health:

• Coenzyme Q10 - Improves scalp circulation. Increases tissue oxygenation. It is also very important for heart health. Take 60 mg daily.

• L-Cysteine and L-methionine

• Two amino acids believed to improve quality, texture, and growth of hair. They help prevent hair from falling out.  Dosage: 500 mg each twice daily, and on an empty stomach.

Diet and Food Therapy for Baldness and Thinning Hair:

• A wholesome diet, rich in silica, calcium and iron, will help reduce or prevent hair loss. Green, leafy vegetables, especially sea vegetables, are good mineral sources. Raw oats provide silica. Dried fruits and cherry juice are rich sources of iron.

• For women, thinning hair or hair loss can be a sign of a problem in the gastrointestinal tract. It could be a sign of insufficient stomach acids; It could also mean a deficiency of protein, zinc and other nutrients. Taking two acidophilus tablets after or between meals (four to six tablets per day) for two months will help.

• For men, balding process can be slowed down by taking a low-fat diet. Some scientists postulate that the male pattern baldness is tied to increased testosterone levels during puberty. A high-fat, meat-based diet raises testosterone levels, and that may adversely affect hair follicles. For example, in Japan, male pattern baldness was very rare prior to World War II when the diet was lean and healthy. The Japanese now consume a more fatty, Westernized diet. Baldness is now increasing substantially among Japanese men. Eating low-fat foods may not stop hair loss; but it might help slow down the hair loss.

• Anemia is one of the most frequent causes of hair loss. Eat plenty of iron-rich foods, like liver (Avoid if you are pregnant) and other organ meat, whole grain cereals, dark green leafy vegetables, eggs, dates, and raisins.

• The hair is comprised mostly of protein. To encourage hair growth, adhere to a diet rich in protein. A recommended diet for this purpose includes calves liver, brewer's yeast, wheat germ, and two tablespoons of granulated lecithin. Along with protein, these foods are also high in B vitamins, an important nutrient for hair.

• European studies have found that soy protein reinforces hair and stimulates its growth. In one study,  The hair growth increased by 15 percent. Due to the link between unfermented soy and breast, stomach and other cancer, use only fermented soy products such as tempeh and miso. Other good sources of protein are: low-fat cheese, eggs, fish, beans, brewer's yeast and yogurt.

• Another important nutrient for hair health is silica. Studies in the former Soviet Union have shown that silica therapy slowed hair loss. Organic silica added to shampoo was found to help prevent baldness, stimulate healthier hair growth and assure beautiful shine, luster and strength. Some scientists claim that they have effectively stopped further hair loss by adding silica to their shampoo. This can be applied externally to regrow already lost hair.

• Silica is found in the outer coverings of potatoes, green and red peppers and cucumbers. Bean sprouts are also high in silica. Eat whole foods including sprouts.

• Vitamin C improves the absorption of iron. Include a good serving of fruits and vegetables in your diet.

• Vitamin E is important for healthy hair growth. Eat avocados, nuts, seeds, and olive oil on a regular basis.

• If hair loss is due to thyroid dysfunction, eat more foods rich in vitamin A and iodine. Eat vegetables such as carrots or spinach in unrefined, cold-pressed seed oils such as flax, walnut or pumpkin seed and sea salt. Take turnips, cabbage, mustard, soy beans, peanuts, pine nuts and millet if there is a deficiency of iodine.