As far as I know Amazon doesn't offer any Free Shipping Promotional Codes nowadays, but if you buy items priced over $25 you can select Super Saver Shipping as your shipping speed and shipping will be free. Still check their website whether they have introduced any free shipping code recently.
Amazon is my most favorite online shopping site. They have huge no of products (one of the largest) arranged professionally so that customers can easily find out what they are looking for. They have pretty quick shipping option, sometimes even within 24 hrs, and moreover the shipping charges will be waived off if the total price of your order is over $25 only.
Amazon introduces promotional coupon codes time to time and many other discount coupon codes on health and personal products, electronics, books, kindle books, and many more. Check the coupons on their site since they update the coupon codes from time to time and will have the most recent new coupons for you. It's worth for your money and time. You can save a lot by using these promotional codes regularly.