There seems to be two approaches you can take here.
The first is to go to a Wingman series at the main Machinima app screen, select the first video, and play it (you can also select the ellipsis [...] at the bottom of a series to get to the entire list). This will automatically play all of the videos in that series. At the time this was written, there are 11 videos in the Need for Speed series, and 15 in the Battlefield 4 series. Simply play through the entire series, and when it finishes (I get a "retry" screen at the end - just select that button and it will take you back to the main screen), play the first video again.
The second option involves adding all the Wingman videos you like - no matter the series - to your Favorites list. Once you've added them, simple play the first one like above, and all of them will play in sequence.
Repeat either process while you are doing other things until the achievement pops (you will get an advertisement after every three videos). While you can also Snap the Machinima app to the side and play the videos, it does not
automatically advance to the next one. You can keep track of your progress in the Smartglass app. The progress you make doing this also counts towards the following achievements: