As far as we know right now, any paperwhite ( 4 GB ) that has not recieved an update from "factory" mode can be jailbroken. ( wither Over The Air or USB update )
I have not had time to update the wiki with this information ( so it only lists the exception of 5.8.9.0.1 ), and knc1 has spent enough time updating his first post, I think we need to try to get more people to use the wiki.
https://wiki.mobileread.com/wiki/5_x_Jailbreak
The firmware download links will take you to google, as the forum member who was hosting them realized enough people had copied them, and stopped paying for hosting.
If your serial starts with G090G1, you shoudl be able to continue using all the files listed in the wiki.
If you have a differnet model number, you may want to compare the wiki steps versus this post knc made for 5.8.9.0.1 ( 5.8.9.0.1 image can be used instead of 5.7.4 image and support more devices like the 32GB manga model ):
https://www.mobileread.com/forums/sh...d.php?t=291336
My understanding is that special offers don't stop the jailbreak, but make it harder (impossible ) to recover if there is some kind of issue , so the recommendation is to pay amazon to remove them, but then you have to connect to the internet. ( you can skip registration, and put the update blocking folder on the kindle, then resume registration to prevent update ).
You skip registration by saying "connect to wifi", but then hitting the little [x] to close the wifi popup. That will give you a "complete registration later" button.