Redirect WordPress Feeds To FeedBurner using Action Hook:
You can use this simple snippet in your function.php to redirect your WordPress feeds to Feedburner. If you try to go to http://sakinshrestha.com/feed, you will be redirected to FeedBurner’s feeds for Sakin Shrestha.

Just open funtion.php file which is located in your theme directory. You can simply add the following snippet in function.php to redirect your WordPress Feed to Feedburner.

//Redirect WordPress Feeds To FeedBurner
add_action('template_redirect', 'ci_rss_redirect');
function ci_rss_redirect() {
if ( is_feed() && !preg_match('/feedburner|feedvalidator/i', $_SERVER['HTTP_USER_AGENT'])){
header('Location: http://feeds.feedburner.com/sakinshrestha');
header('HTTP/1.1 302 Temporary Redirect');
}
}
In the above code you just need to replace http://feeds.feedburner.com/sakinshrestha with the FeedBurner URL.

There are other methods as well. For this you can Read More