both ip and domains should work, the client will resolve hostnames. I use a public .org dyndns, which gets bounced through my own ip, then back out to a faster .com domain. so my redirect actually redirects to a redirect of a redirect

, and it works fine.
if your files are hosted on a public site, try to download them through a web browser. type out the full url (case sensitive), and if it works there it will work for the game. could be that you have a typo somewhere, or pointing to the wrong root directory above your kf files.
if your files are hosted through your own httpd, then have someone else on the outside try and download them through a browser from you, or use a link checking site to test. since your isp may be blocking incoming http ports, which would not be obvious through a request from your own ip. this was the case for me, and I had to change the port on my http server for public connections to get through.
you can also use this site to test your urls, it will confirm that your files are publicly reachable in either case:
http://www.websitepulse.com/help/tools.php
just enter the url of a file in question same way as above, and it will simulate a full download from you on their servers, posting http header results to make sure everything is working right. try to choose a smaller file for faster responses, it will report transfers down to the byte. it's been very useful to me for quickly testing any changes I have made, to see that things have transfered properly once they get uploaded.