Enqueue Style for a page/pages only

It should work like this.

Sidenotes: I don’t know why you deregister a stylesheet and register it again. Also: get_bloginfo('template_directory') is now replaced by get_template_directory_uri(). Third: Are your folders really named with dots in between? Maybe this causes problems. And maybe your ui stylesheet is an dependency of the main jquery ui stylesheet.

You should also start accepting answers on your questions. Your “accept rate” of 67% will people hold back from answering your Qs.

function wpse_16487_enqueue_styles()
{
    if ( is_page('Add Event') ) // also tried slug, page id and wp_reset_query(); bot not worked
    { 
        wp_register_style( 'jquery-ui-custom-flick', get_template_directory_uri().'/styles/jquery-ui/ui-custom-flick.css', 'jquery-ui' );
        wp_enqueue_style( 'jquery-ui-custom-flick' );
    }
}
add_action( 'wp_print_styles', 'wpse_16487_enqueue_styles' );

If something’s not working, you should start debugging your wp query: echo '<pre>'; print_r($GLOBALS['wp_query']); echo '</pre>'; and check for the page name/slug to register it.