Codeigniter query will return result in associative array and in_array() function will not going to do the trick.
Here is one way you can do this custom is_in_array function source
//Helper function
function is_in_array($array, $key, $key_value){
  $within_array = false;
  foreach( $array as $k=>$v ){
    if( is_array($v) ){
        $within_array = is_in_array($v, $key, $key_value);
        if( $within_array == true ){
            break;
        }
    } else {
            if( $v == $key_value && $k == $key ){
                    $within_array = true;
                    break;
            }
    }
  }
  return $within_array;
}
$array = $rs->result_array();
if(!is_in_array($array, 'Nick', $data['Nick']))
{
    $this->db->insert('cms_cart_customers', $data);
}
Other Method
If you are trying to avoid duplicate entry, you should use a Select query first to check that the 'Nick' = $username is already present in table, if not then Issue an insert
Example
$rs = $this->db->get_where('cms_cart_customers', array('Nick' => $username));
//After that just check the row count it should return 0
if($rs->num_rows() == 0) {
    $this->db->insert('cms_cart_customers', $data);
}