Adding this in your theme’s functions.php removes the RSS meta link markup on all pages of your wordpress site, which means browsers won’t be able to detect any RSS feeds on your pages:
add_action( 'wp_head', 'wpse58023_wp_head', 1 );
function wpse58023_wp_head() {
// Removes main feed link(s)
remove_action( 'wp_head', 'feed_links', 2 );
// Removes comments feed link
remove_action( 'wp_head', 'feed_links_extra', 3 );
}
For instance, the above function removes this markup on home page (feeds differ on different pages):
<link rel="alternate" type="application/rss+xml" title="My Website Feed" href="https://wordpress.stackexchange.com/feed/" />
<link rel="alternate" type="application/rss+xml" title="My Website Comments Feed" href="http://wordpress.stackexchange.com/comments/feed/" />
So now, browsers will think that your home page has no feed. What you can then do is, add something like this in your header.php (before the </head> tag):
<link rel="alternate" type="application/rss+xml" title="My Website Feed" href="http://feeds.feedburner.com/mywebsite" />
Use conditional tags to show different feeds on different pages. That should give you an idea as to what you can do.