Zombies, Run! works just fine on treadmills - we can use your device's accelerometer to track paces and to initiate zombie chases. However, given that you will not be moving in real space, we will be unable to show you a map of your run on ZombieLink.
In order to use Zombies, Run! on a treadmill, all you need to do is tap the Tracking button and choose Step Counter tracking rather than GPS tracking. Ensure that you keep your phone with you (e.g. in your hand or pocket) so that the app can pick up your movement.
Please read How do I calculate my stride length? to ensure the tracking is as accurate as possible.