Hide image if taxonomy term is empty

Instead of write manually the html code for your flags, you should create it using php and wordpress functions:

$countries = get_terms('country', array('hide_empty' => true) );
$exclude_terms = array('featured');

if ( ! empty($countries) && is_array($countries) ) { ?>

  <img class="mapAdjust" src="https://wordpress.stackexchange.com/questions/114245/<?php bloginfo("template_url'); ?>/img/map-adjust.gif" />
  <img class="map" src="https://wordpress.stackexchange.com/questions/114245/<?php bloginfo("template_url'); ?>/img/map.jpg" />

  <?php
    foreach ( $countries as $country ) {
      if ( ! empty($exclude_terms) && in_array($country->slug, $exclude_terms) ) continue;
      $name = esc_attr($country->name);
      $slug = $country->slug;
  ?>

    <div class="flag<?php echo str_replace(' ', '', $name); ?>">
      <a href="<?php echo get_term_link($country, 'country') ?>" alt="<?php echo $name; ?>" title="<?php echo $name; ?>">
        <img class="flag" src="https://wordpress.stackexchange.com/questions/114245/<?php bloginfo("template_url'); ?>/img/flags/<?php echo $slug; ?>-flag.png" />
      </a> <!-- <?php echo $name; ?> -->
    </div>  <!-- /flagCont -->

  <?php
  }
}

I’ve used only 2 functions: