Jailbreaking 5.6.1.1. itself is possible...... And some TLS or SSL certs needed by Kindle are there in 5.6.1.1. only. You wont probably be getting an update after 5.6.1.1. @knc1's software jailbreak can do it.
EDIT: FOUND IT NOW THAT FACTORY DOWNGRADES DONT WORK ON PW1
Sorry, knc1