There is a PW3 jailbreak specific to firmware 5.9.6.1 the is discoverable by searching on the tag "pw3 jailbreak"
https://www.mobileread.com/forums/sh...d.php?t=313086
Update to 5.9.6.1 than apply the jailbreak. 5.8.11 is the last to support kindlets so you might want to downgrade to that later.