Generally speaking, they auto update, and the latest firmware is always patched to not be jailbreakable. However airplane mode easily dodges the auto update process, and new vulnerabilities are found to enable jailbreaking eventually.
When I bought mine, it was updated to the latest firmware. I wanted to jailbreak mine, the method was “there isn’t one yet” so I set it in airplane mode. For a bit I manually copied all books over usb to the kindle, or disabled airplane mode to read new books if there wasn’t a new firmware version out yet anyway. A few months later, there was a jailbreak method. Now ive jailbroken. I can even connect it to the internet, and auto updates are prevented.
If the kindle is old enough it doesn’t recieve updates anyway though, then it should be very easy.