Zombies, Run! 5k Training is not a music player, so you cannot add music to the app, or create playlists within it. We can only access playlists that already exist on your phone, the same way other fitness apps do.
We're aware that Zombies, Run! is not compatible with all music apps for Android. As such, playlists created in some apps will not show up and it is not possible to used streamed playlists. In particular, we know that the app does not work well with Google Play Music. We've spoken directly with Google and they have told us their API does not support the integration that we require so unless something changes in the future this isn't a problem we can fix, unfortunately.
We generally recommend that players use Shuttle on their phone to create their playlists, as it's the most reliable music app for use with Zombies, Run! You can try using the Shuttle music app here, or the Music Player for Android here. These are both fairly basic music players but will work with Zombies, Run!