This offer is only for those with a Kindle Fire with Special Offers (KFSO).
From the home page of your KFSO, swipe the top menu to the left until you see Offers, then press/click in order to see the current offers. At the bottom, you should see the offer for $30 Off a Purchase of $100 or More in the Amazon Denim Shop. Click on the offer, then on the orange button to add the credit directly to your account. It's nearly instant and the next screen offers to take you to Amazon so you can spend that credit away! If you miss that screen, though, don't worry - a document about the offer will appear on your home page. You must sign up by October 16.
Choose one or more items in the Amazon Denim Shop, place them into your cart and checkout (using the full checkout process, not one-click). You only get a single credit and the purchase must be over $100, but you can add a few pairs of jeans together to get to that total.
This credit expires October 23. Limit one per customer and one per device.