Since Pocket isn't available on Amazon's App Store, you'll need to sideload the APK and install it that way. Basically it means is taking the install file for Pocket, transferring it to your computer and from there onto the Kindle over USB, enable installations from Unknown Sources in settings, and install it.
If the article looks like gibberish to you because you aren't yet familiar with this part of using Android do say so and I can try and help. The Amazon App Store's selection is horrible in general so you will want to learn the process of sideloading anyway, I assure you.
I already have the Pocket APK extracted anyway so I've thrown it up here in my Mediafire public folder so you can download it: Pocket 2.7 APK