How to access variables from Functions file in theme files

Whilsts @Shaon’s answer is perfectly valid, I’m of the opinion you really shouldn’t be throwing configuration settings around as global variables – use a constant instead.

/* Constants are in the global scope, but can only be defined once. */
define( 'FEEDBURNER_USERNAME', 'my_username' );
define( 'FEEDBURNER_PASSWORD', 'my_password' );

If the variable needs to be dynamic (for example, if it’s an option in the database), use a function that returns it:

function get_feedburner_config( $option = null )
{
    $config = get_option( 'feedburner' );
    $config = wp_parse_args( $config, array(
        'username' => 'default',
        'password' => 'default'
    ));

    if ( $option )
        return isset( $config[ $option ] ) ? $config[ $option ] : '';

    return $config;
}