Use a cookie to determine if the user has previously submitted the form and stop him from resubmitting for a determined period.
<form action="" method="post">
   Dogecoin-address:  <input type="text" name="address"/><br>
   <input type="submit" name="submit" value="submit">
</form>
<?php    
  if(isset($_POST['submit']) && !isset($_COOKIE['sumbission_cookie_name']) ){ //check if form was submitted & if it's a new submission
    setcookie('sumbission_cookie_name', TRUE, time() + (60*60), "/" ); // expires in 1h
    if (isset($_POST['address'])) {
    }
    $url = 'example.com'. $_POST['address'];
    $data = array('key1' => 'value1', 'key2' => 'value2');
    // use key 'http' even if you send the request to https://...
    $options = array(
                    'http' => array(
                       'header'  => "Content-type: application/x-www-form-urlencoded\r\n",
                       'method'  => 'POST',
                       'content' => http_build_query($data)
                    )
                  );
    $context  = stream_context_create($options);
    $result = file_get_contents($url, false, $context);
    if ($result === FALSE) { /* Handle error */ }
    //ob_start();
    var_dump($result);
    //$output = ob_get_clean();
    // later:  $message = "Success! You entered: hygtfrd".$input;
  }    
?>
</body>
</html>
In case the user is coming back to the page and you want him to be able to submit the form again (before the 1h cookie expires), you should add an exception for this to remove the cookie and the code will look like this:
<form action="" method="post">
   Dogecoin-address:  <input type="text" name="address"/><br>
   <input type="submit" name="submit" value="submit">
</form>
<?php    
  if( isset($_POST['submit']) ){ //check if form was submitted
    if( !isset($_COOKIE['sumbission_cookie_name']) ) { // check if it's a new submission
      setcookie('sumbission_cookie_name', TRUE, time() + (60*60), "/" ); // expires in 1h
      if (isset($_POST['address'])) {
      }
      $url = 'example.com'. $_POST['address'];
      $data = array('key1' => 'value1', 'key2' => 'value2');
      // use key 'http' even if you send the request to https://...
      $options = array(
                      'http' => array(
                         'header'  => "Content-type: application/x-www-form-urlencoded\r\n",
                         'method'  => 'POST',
                         'content' => http_build_query($data)
                      )
                    );
      $context  = stream_context_create($options);
      $result = file_get_contents($url, false, $context);
      if ($result === FALSE) { /* Handle error */ }
      //ob_start();
      var_dump($result);
      //$output = ob_get_clean();
      // later:  $message = "Success! You entered: hygtfrd".$input;
    }
  }   
  else {    
    setcookie('sumbission_cookie_name', TRUE, time() + 1, "/" ); // expires in 1s
  } 
?>
</body>
</html>
This last example will make the cokie expire in 1 second and will let him submit the form again.