The update adds faster cover loading and it reportedly also fixed the sensitivity issue that some have experienced when using the volume buttons as page turn buttons. According to the changelog readers also have greater font choices, which strange because I can't seem to find any options for font choices.
Amazon is also promising auto-brightness controls, meaning that the Kindle app is now integrated with the auto-brightness option for your Android device. Unfortunately I have the brightness set manually on my Hisense Sero 7 Pro, and the Kindle app completely ignores the setting. I have to manually adjust the brightness inside the app as well as outside the app, and it's getting to being annoying.
You can find the app in Google Play and other fine app stores.
Here's the change log: