There has been no shortage of jailbreak solutions for the Amazon Kindle; some last only a few months before being rendered inert by a software update. A new jailbreak called Sanctuary has just been released, and it works on any Kindle model running firmware 5.16.4 to 5.18.3.
Unlike most jailbreak methods, which require complex software and coding, Sanctuary is browser-based and works in the Kindle Silk browser right on the Kindle. It does not require registration and also works on blacklisted kindles to. It uses the new jb.sh, so you do NOT need to manually install the hotfix or block OTAs after jailbreaking; it is all handled for you.
Why should you jailbreak your Kindle with this new method? You can install 3rd-party apps, such as K-Reader, to replace the stock Kindle app. Custom screen savers are also available, which allow you to upload your own to the device.