Hi,
It's indeed the file "listing" of the view "order" that you want to edit. Make sure that you're editing it for your backend template and not your front end template as otherwise, it would be the order history of the customer on the frontend you're editing.
You can use such code:
<?php echo $row->order_discount_code; ?>
Note however that the partner information isn't there. It's added dynamically by the HikaShop affiliate plugin thanks to the triggers of HikaShop.
If you really want to add it to the partner column, you would have to add your code in the function showField of the file plugins/system/hikashopaffiliate/hikashopaffiliate.php
But I would recommend adding it to order/ listing.php view file, in another column. Otherwise, you'll have to reapply your change after each update of HikaShop.