I was having the same problem, and came across this thread. I know it's a couple of months old, but maybe this can help someone.
My Mac wouldn't mount my Kindle Fire HD, so I searched and found this Amazon support page:
This will lead you to download an Android app at:
The file transfer utility will let you move files to and from the KF. It still won't let Calibre see the device, but at least I can drag/drop books to it.
Tried to install the Calibre Companion app, but Amazon says it's not compatible with the KFHD... Have yet to try the Calibre server.
Hope this helps!