I am Your User suggested a method to eject your Kindle in Linux. While his method works, you don’t need to specify the partition number. E.g.
$ sudo eject /dev/sdd
where /dev/sdd is the device file of the Kindle.
But what if you want to reconnect it back without plugging in and out the usb cable? You can add the -t switch.
$ sudo eject -t /dev/sdd
Even though it prints the following error:
eject: CD-ROM tray close command failed: Input/output error
it works, and the Kindle reappears in KDE.