When you start a match or after you die you're at the spawn screen where you can press
to Start or
to Partner Start. Now assuming you have a partner go down to 'Hands' and set yours as your Partners hand and start the match either way. The game always assigns me a partner automatically.
Now this will count as one but the game will not count another until you either change back to yours and use it and then back to your partners and use it again OR when you start a new match and set the partner hand again. Jrocker23 notes that not changing back worked for them.
This does not have to be done in one match as it is cumulative for the times you use the hand, you also do not need to have unlocked the perks your partner has to use their card.
Here's a video of me using a partner's, switching to mine and then back to my partner's