Amazon Underground pays the app developer for the duration of usage of the app, and so needs to track how long you are using the app for. Perhaps it needs data tracking enabled to identify the duration of usage?
(For those who haven't read the article: The author only discovered this because they have CyanogenMod and a permissions blocker installed and in use. Most people wouldn't be told they were being tracked.)
https://www.amazon.com/gp/feature.html?ie=UTF8&docId=1003016...