I have Calibre content server running and am able to access it via my Kindle - here is what I did high level
1. Get the content server running with the GUI and use port 8080 username and password
2. Install xampp (to get Apache running on my windows box) CONFIRM the service is working
3. Follow instructions for Content Server Reverse Proxy (in help files)
http://manual.calibre-ebook.com/server.html
4. Start content server from command line as stated in Revers Proxy instructions (used a *.bat file on win box)
5. Added a launch page index.php in Apache that has links to full Library site and the Mobile version
6. Access the launch page then navigate to the content servers mobile page from kindle (enter username pw)
7. Remember to forward appropriate ports on your router
8. I use dyndns because I have a dynamic IP address
9. Adding a PHP script to log what IP address access my launch page
The issue appears to be that the Kindle browser doesn't like pointing to a port :8080 or anything for that matter. Simply setting the Content server to port 80 didn't fix the issue, I had to go all the way and use Apache and the Reverse Proxy stuff. Took about 20 minutes.
Haven't had any issues since implementing this solution