We're big fans of streaming music players like Spotify, Pandora and Amazon Music here at Six to Start, and we understand that it would be great to be able to use them in conjunction with Zombies, Run! We have contacted them directly, but we are unable to integrate them with Zombies, Run! for legal reasons as their licensing and Terms of Service prohibit this.
It’s possible in the main Zombies, Run! app to use these services externally to the app rather than integrating directly. However, this is only possible because the main app uses a newer code base and only works on phones which are able to run iOS 7 and above or Android 4.0 and above. This is a feature which will be included when the 5k Training app is updated.