Please do release a new video! There’s a comment thread about “it’s a pity kindles don’t seem to get jailbroken” so presumably some people are confused (me included)
Yea, the video is 7(!) years old, Amazon regularly patches jailbreaks just like Apple does, and for certain fire tablets it’s apparently impossible to jailbreak fully at all for the last 2 years. So you either need to find one that didn’t get the OTA update or find some way to downgrade to a previous OS/bootloader.