Style file inclusion

You need to hook it to an action.

Add the below code to the theme’s functions.php file. It should work.

add_action( 'wp_enqueue_scripts', 'theme_flexslider_css' );
function theme_flexslider_css() {
    wp_register_style( 'flexslider', get_template_directory_uri() . '/css/flexslider.css' ); 
    if( is_page( 'home' ) ) { 
        wp_enqueue_style( 'flexslider' ); 
    }
}