You can try this code saving it as extension (FeedburnerImgFixer.cs):
[Extension("Converts image path from relative to absolute URL for FeedBurner", "1.0", "BlogEngine.NET")]
public class FeedburnerImgFixer
Post.Serving += Post_Serving;
static void Post_Serving(object sender, ServingEventArgs e)
if (e.Location == ServingLocation.Feed)
var relativePattern = "src=\"" + Blog.CurrentInstance.RelativeWebRoot;
var absolutePattern = "src=\"" + Blog.CurrentInstance.AbsoluteWebRoot;
e.Body = e.Body.Replace(relativePattern, absolutePattern);
This should replace any "src" references from relative to absolute in feeds only.
You can check if it works by going to "/syndication.axd".
For FeedBurner to pick it up will take some time, they cache and sync on schedule.