It's your RSS feed, not Feedburners, and how to maintain the relationship with your readers through your RSS feed
There are many services which offer services related to RSS or Atom feeds. These services usually consume your feed, modify it, and republish that feed on a different URL. Feedburner is only one of many such services, most of whom perform valuable features to web site authors.
The RSS or Atom feed published by a website is the medium through which your readers track new content on your site. Ideally readers of your site see that big orange button with the curved lines and know it is a URL they can paste into blog aggregator software and use it to track updates on your site. That's what we want, readers who track your site and return to it from time to time.
It is important that your RSS (or Atom) be known by a URL you control. Why?
As I said above these services republish your feed on a URL which they control.
What might happen is that readers subscribe through a URL controlled by the service. What happens then if you decide to stop using that service and maybe use another? That new service will use a different feed URL. That means the existing subscribers will be left behind on the old URL, unless you can convince them to change their subscription.
That's why it's best for your feed URL to be under your control.
In Feedburner's help this exact situation is discussed: If I redirect my Blogger feed to FeedBurner, should I change my blog's feed chicklet links, too? .. To summarize: Redirect your feed, but retain your original address for the links you promote. however the question is bigger than both Blogger and FeedBurner. The question applies to any software that exports RSS feeds, and it applies to any service that improves feeds.
The best practices recommendation given by Feedburner is to promote your standard feed, but in the server configuration make the feed URL a soft redirect to the URL provided by Feedburner. If your standard feed URL is http://example.com/feed/ and the Feedburner URL is http://feeds.feedburner.com/MYFEEDADDRESS by all means continue promoting http://example.com/feed/ as your feed URL. A soft redirect quietly make any request on your regular feed URL make the request from the redirected URL.
The method they give is a little complex and depends on the Apache web server and depends on you having an ability to edit the Apache configuration. It's not always possible to do this. It may be that your website software includes the required soft redirect functionality. For instance the Drupal Feedburner module has that capability. I recommend looking for this feature in the software rather than the more complex route of configuring this in Apache.