This is your problem right here
Code:
IOError: [Errno 13] Permission denied: u'/Volumes/Kindle 3/metadata.calibre'
You have a permission error witht he file metadata.calibre that's on your Kindle. Try deleting that file and see if it works. Also with the Kindle plugged into the USB port, (without Calibre running), check the Kindle filesystem for errors. Also check the permission for /Volumes/Kindle 3/ and see what's going on.
This is not a Calibre problem. It's something either on your computer or the Kindle.
Another thing to try is to give a factory format to the Kindle and then see if it works from there.