I can't take credit for this one, just a satisfied user: Drupal and FeedBurner shows you how to easily hook your Drupal RSS feed into FeedBurner.

Quick summary (see link above for details):

• Create a URL-alias for rss.xml, name it something like feedburner-feed
• When you register your site with FeedBurner, give it the aliased feed, for example I used http://boodebr.org/feedburner-feed
• Redirect existing feed subscribers by adding this to your site's .htaccess:
  # redirect feed requests to feedburner
  # (see http://www.roguewolves.com/drupal-and-feedburner)
  RewriteCond %{HTTP_HOST} boodebr.org
  RewriteRule rss.xml http://feeds\.feedburner\.com/boodebr-org [R,L]
  RewriteCond %{HTTP_HOST} boodebr.org
  RewriteRule node/feed http://feeds\.feedburner\.com/boodebr-org [R,L] 

I have Drupal configured as described here: Having Drupal live in a subdirectory. I was able to just add the above lines to the end of my existing .htaccess.

All existing subscribers will be transparently sent to feedburner, as will new subscribers. This redirection magic is really nice if you ever stop using feedburner — just remove the lines from .htaccess, and the feed is back on your site.