After Feedburner offered their MyBrand (and TotalStats) features for free, I contacted Feedburner for MyBrand feature activation. And today, I got an email informing that it has been enabled for my accounts. I sent my request on July 5th and I got this feature activated today, July 7th. Thank you Google!
To use this feature, you need to have access to your domain DNS records. The only thing you need to do (after having this feature enabled) is add a new CNAME record for your domain. I want to use something like http://feeds.orangescale.com/OrangescaleJournal instead of http://feeds.feedburner.com/OrangescaleJournal. So, I add a new record for my domain:

feeds CNAME feeds.feedburner.com.

If you want something other than feeds.yourdomain.com e.g. rss.yourdomain.com, you only need to change the feeds.
Everything should work now. About this MyBrand feature, you need to know first that:

• You need to have access to your domain DNS management. If not, contact your hosting provider/domain registrar.
• If you have CNAME functionality, both feed addresses will work. You can have two feeds URL; they are the same. This CNAME is for redirection.
• You can add up to 5 domains in your MyBrand page feature (for every single Feedburner account).
• Yor branded RSS addresses are based on your feed address generated from Feedburner. So:
  • http://feeds.feedburder.com/MyBlog will be http://feeds.yourdomain.com/MyBlog
  • http://feeds.feedburder.com/OtherBlog will be http://feeds.yourdomain.com/OtherBlog
  • http://feeds.feedburder.com/myblog/one will be http://feeds.yourdomain.com/myblog/one

I personally love this feature. If you want it too, just make a request. If you think this feature is useless, because the original feed URL looks good for you, you have the option not to use this feature.