Good step by step explanation how jailbreaking works.
An addendum:
a) There's an important difference between "out of the box" firmwares (brand-new devices) and (OTA/sideload update) user firmwares. Only the latter may not be jailbroken if > 5.8.7. As it looks now, nearly all OOTB fw versions may be jailbroken - including some (or even all?) 5.9.x variants.
b) There's no need to register a still selling "legacy" Kindle of 7th and 8th generation (PW3, KT3, KOA1, ...) - just keep WiFi off (airplane mode) and connect it via USB to a computer. If you can access it as external storage, just create the OTA blocking directory and try the downgrade to the factory test fw.
Your method (registering it, then switch off WiFi immediately to avoid the very aggressive auto update) is only needed for 9th generation Kindles (namely KOA2) where without registering it first, it's not even possible to access its storage via USB, which is a necessary prerequisite for the jailbreak.