First things first - -
Check your Kindle/Firmware combination to see if
;fc-cache
in the search bar works.
That is required to be working for the 5.6.5 jb to be used.
And disabling that is what Amazon/Lab126 did to 'fix' the Kindles against this jail break.
I.E: They did not fix the browser exploit, just one of the jb requirements.