Why can't I change my skin?

Solution 1:

  1. Insure you have Minecraft PE 0.11.x+
  2. Search "Skins for Minecraft" in the kindle App Store, and then click an app.
  3. Install the app, and open it up.
  4. Click the head of the skin that you like the best.
  5. Click the "Download Skin" button.
  6. Open up minecraft, and you will see that your skin has changed!

Source: Wikihow