Are you, by any chance, using macOS or Linux?
If you're on Linux, make sure to start Calibre before you connect your Kindle, because it's using MTP and only 1 application can use MTP at the same time. By default, this will be your file browser, so boot up Calibre first.
If you're on macOS, you need an application for MTP. Either the
official app or openMTP. Both work fine.