If you have a Kindle that is recent enough to still get updates, chances are it can't be jailbroken right now and you should prevent it from automatically updating if you ever want to have a chance at jailbreaking it. There are no known exploits to jailbreak the most recent Kindle firmwares (>= 5.18.6) and if one is discovered, Amazon will likely release a firmware that patches it shortly afterwards.
In order to prevent updates, first connect your Kindle to a PC and delete already existing update files, if there are any (named update-???.bin or similar). Then you have essentially two options:
- keep your Kindle permanently disconnected from the internet
- fill your Kindle's storage with (junk-)files until there's not enough storage left for update files
See here for more info on preventing updates.
After your Kindle is successfully jailbroken, you can delete the junk-files and reconnect it to the internet without any issues.