If you are unable to re-download Zombies, Run! after having deleted it, it's likely because your device is no longer compatible with the game. Unfortunately, Zombies, Run! 3, and Zombies, Run! (Free) are only available to users with devices running Android 4.0+.
This was a difficult decision for us, but in order to make Zombies, Run! on Android as stable and advanced as we wanted it to be, it was necessary for us to limit the app to these versions of Android.
Please Note: If you are running Android 4.0+ and previously purchased Zombies, Run! 3 but are having trouble re-downloading, please go to our FAQ page about restoring Legacy Status here: I'm A Legacy User - How Do I Upgrade Without Losing My Access To Missions?