Unless you have access to the server that setup their /feed to use feedburner, you won't be able to change anything on your end.
The concept is pretty simple:
you have a /feed that gives you the feed of the website as expected
you have a small setup in Apache (or equivalent HTTP server) to tell to redirect the user if he's not a feedburner server; so the feedburner can read the /feed data directly, anyone else can't.
However, I don't see why you think this is a problem. The data you get is exactly the same. Only you get an intermediate 301 when retrieving the data using the original /feed path.
There is same examples on this website on that's achieved (.htaccess or a PHP snippet):
http://codex.wordpress.org/Using_FeedBurner
If the test used by the server with the /feed only checks the User Agent name, then you could simulate being feedburner. But again, you will have much more chance to connect and read the data using feedburner (because that's owned by Google and they have the horse power to send you the content of the feed without an inch of a problem.)