The e-ink kindles don't use adb (*Android* debug bridge) at all. They aren't Android-based. Some models have known ways to bring them into a SoC-based mode where things can be flashed to the device (which allows to flash a new root filesystem or the like).
No such way is known for the KPW (yet).
Indeed there probably *is* a factory cable, at least I found traces of such in the bootloader code and the PMIC (which handles ID-codes on USB cables) documentation seems to indicate so. However, all I found then is a different code path in the PMIC setup, which will only trigger that the device is supposed to be bus-powered (instead of using the battery). I've not found traces of code that suggest that the device would offer debug access.
The Kindle Paperwhite *does* offer access through its serial port. That however is fiddly, requires opening the case and to solder cables to some really tiny pads.
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