The best way is to search for R availability, and when at least 1 opens up, make your partner your travel nominee, and grab that seat. Then wait and hope that a second one will open up for you. The advantage of this approach is that the partner without status will get the upgrade and you will more likely clear at the gate if not before. Other way round your partner will likely be left in the back.
If the flight is after Jan 11th and you are on a widebody, then it may be worth calling in to up-buy to a PE seat as 1) that has higher upgrade priority than Flex and 2) if the upgrade doesn't come through it ain't so bad. If the flight is <= 11 January however, you want to stay in Flex and use the enhanced (3 week) upgrade window available for Flex, which is apparently not available for PE.