Flatfish or flounder fish is a low fat, mild tasting fish, and according to the FDA is a safe choice for pregnant women. It is rich in vitamins and minerals like niacin, B-vitamins, phosphorus, calcium and selenium. Selenium is essential to regulate the immune and thyroid function of expecting mothers. Calcium is required for the bone development of the baby. Having flatfish also aids the growth of healthy heart, muscles and nerves in your baby.