Let us amend that to -- it is impossible, unless you are willing to pry open your Kindle and insert probes into its innermost guts and apply the jailbreak scripts over a serial port.
In other words, there is no news on that front. But if and when a jailbreak is discovered, it will be announced to great fanfare on the master jailbreak thread:
https://www.mobileread.com/forums/sho...d.php?t=186645
Now, if you were jailbroken, it would be a simple matter of installing the Rescue Pack, rebooting the Kindle into the ssh-enabled diags partition, ssh'ing into the Kindle and flashing the correct system images to the main partition via the command-line and the magic of
dd -- which there are already guides for.