How to save dismissable notice state in WP 4.2?

There’s no need for a library, it’s fairly straightforward to accomplish. If you are coding your own plugin (which it appears you are), then you can do this in a fairly lightweight way:

A slightly modified version of the notice, which checks if it’s been dismissed before displaying, and stores the “type” of notice in the markup for access in javascript:

function prefix_deprecated_hook_admin_notice() {
    if ( has_filter( 'prefix_filter' ) ) { 
        // Check if it's been dismissed...
        if ( ! get_option('dismissed-prefix_deprecated', FALSE ) ) { 
            // Added the class "notice-my-class" so jQuery pick it up and pass via AJAX,
            // and added "data-notice" attribute in order to track multiple / different notices
            // multiple dismissible notice states ?>
            <div class="updated notice notice-my-class is-dismissible" data-notice="prefix_deprecated">
                <p><?php _e( 'Notice', 'my-text-domain' ); ?></p>
            </div>
        <?php }
    }
}

add_action( 'admin_notices', 'prefix_deprecated_hook_admin_notice' );

And then, the following jQuery

  // shorthand no-conflict safe document-ready function
  jQuery(function($) {
    // Hook into the "notice-my-class" class we added to the notice, so
    // Only listen to YOUR notices being dismissed
    $( document ).on( 'click', '.notice-my-class .notice-dismiss', function () {
        // Read the "data-notice" information to track which notice
        // is being dismissed and send it via AJAX
        var type = $( this ).closest( '.notice-my-class' ).data( 'notice' );
        // Make an AJAX call
        // Since WP 2.8 ajaxurl is always defined in the admin header and points to admin-ajax.php
        $.ajax( ajaxurl,
          {
            type: 'POST',
            data: {
              action: 'dismissed_notice_handler',
              type: type,
            }
          } );
      } );
  });

In PHP, set up the AJAX hooks to capture the AJAX call:

add_action( 'wp_ajax_dismissed_notice_handler', 'ajax_notice_handler' );

/**
 * AJAX handler to store the state of dismissible notices.
 */
function ajax_notice_handler() {
    // Pick up the notice "type" - passed via jQuery (the "data-notice" attribute on the notice)
    $type = self::request( 'type' );
    // Store it in the options table
    update_option( 'dismissed-' . $type, TRUE );
}

And that’s it! No library needed – especially if you’ve already got PHP and javascript files loading.

This method is per the WordPress Core dev team blog