Using action hook to add custom taxonomy to form.

///////////////   MEDIA CUSTOM TAXONOMY    /////////////////////

/**
 * First, create a form section for WP User Frontend
 * with the fields relative to the custom taxonomy
 * in a function 'wpufe_anecdote_media'
 */

/**
 * Add media dropdown to the add anecdote area
 *
 * @uses wpuf_add_post_form_description action hook
 *
 * @param string $post_type the post type of the post add screen
 * @param object|null $post the post object
 */

function wpuf_countries( $post_type, $post = null) { ?>

    <label for="anecdote-media">Countries</label>

    <?php
	    // Add security nonce check
	    wp_nonce_field( __FILE__, 'nonce-countries' );

	    // Get all media taxonomy terms
	    $countries = get_terms('countries', 'hide_empty=0'); //$countries = wp_get_object_terms( $post->ID, 'countries', array('fields' => 'ids') );
    ?>

    <li>

    <?php

    // You can also use the included dropdown generator function of wordpress, but I'd prefer to code the select myself in order to avoid possible problems
    //wp_dropdown_categories('taxonomy=countries&hide_empty=0&orderby=name&name=post_media&show_option_none=Select media&selected='.$countries[0]);

    ?> 

    <select name='post_media' id='post_media' multiple class="requiredField form-control selectpicker">
	    <option value='' <?php if (!count($countries)) echo "selected='selected'";?>>Select a media</option>
	    <?php
			foreach ($countries as $country) {
		        $selected = (has_term($country->slug, 'countries', $post->ID)) ? ' selected="selected" ' : '';
				echo "<option value='" . $country->name . "' " . $selected . ">" . $country->name . "</option>\n";
			}
	    ?>
    </select>    

    </li>
    <?php
}
add_action( 'hook_countries', 'wpuf_countries', 10, 3 );

/**
 * Validate existence of the media after anecdote creation/edit
 * If the select is empty, it returns an error message
 *
 * @uses 'wpuf_add_post_validation' filter
 *
 * @param array $errors errors array
 * @return array errors array
 */

function wpufe_media_validation( $errors ) {
    if( $_POST['post_media'] == '' ) {
        $errors[] = 'Please select a media for your anecdote';
    }

    return $errors;
}
add_filter( 'wpuf_add_post_validation', 'wpufe_media_validation' );
add_filter( 'wpuf_edit_post_validation', 'wpufe_media_validation' );

/**
 * Input the media data after submitting
 */

if (function_exists('wpuf_countries')) {
    add_action('save_post', 'save_media_data');
}

/**
 * Save the media taxonomy data
 */

function save_media_data($post_id) {
// verify this came from our screen and with proper authorization.

 	if ( !wp_verify_nonce( $_POST['nonce-countries'], __FILE__ )) {
    	return $post_id;
  	}

  	// verify if this is an auto save routine. If it is our form has not been submitted, so we dont want to do anything
        // maybe you'll find this unnecessary since there is no possible autosave in the frontend
  	if ( defined('DOING_AUTOSAVE') && DOING_AUTOSAVE )
    	return $post_id;

  	// Check permissions
  	if ( 'request' == $_POST['post_type'] ) {
    	if ( !current_user_can( 'edit_page', $post_id ) )
            return $post_id;
  	} else {
            if ( !current_user_can( 'edit_post', $post_id ) )
            return $post_id;
  	}

  	// OK, we're authenticated: we need to find and save the data

  	$post = get_post($post_id);
	if ($post->post_type == 'request') {
		$country = $_POST['post_media'];
		wp_set_object_terms( $post_id, $country, 'countries' );
	}
}