Simply watch one of the shows produced by Amazon, such as "Alpha House" and "Betas." Both of these shows are located on the home screen of the app currently. Watching one of these shows also stacks with the genre achievements for the app.
It can be done in Snap mode as well, but stating the Amazon App, starting the show, returning to your game, and using the Snap command.
Like the others, it can also be unlocked by fast forwarding to the last minute or so and letting the credits run until the show ends.
EDIT: Here is a possible solution to the glitch, according to Greyfalken:
"I can confirm that this works now, though it looks like it may only pop on something you haven't watched before. I loaded up Alpha House (which I'd seen already) and didn't get credit, but then I tried Betas (which I had never watched) and it worked. If you've already watched both of those shows, you might try one of the Amazon Originals Kids series: Creative Galaxy, Annebots, or Tumbleaf. I have no idea if they count for the challenge and unfortunately I can't check now that I've completed it."