Unable to display favicon using get_favicon()?

You can’t ( and shouldn’t ) have php in your css files, css should be static and unchanging. If you need to generate dynamic css, you can put it inline in the header, or have your theme add a url via wordpress from which to generate the css stylesheet dynamically.

add_action('wp_head',createfunction("","echo '<style>.rss a { background-image: url(".esc_url ( $item->get_favicon() )."); }</style>';"));

If you made the CSS PHP executable, the browser could ( and probably will ) cache the stylesheet making the icon incorrect on some pages when using multiple feeds. It would also be a security issue.