It is currently not possible to trigger Over-The-Air Installs using the server-side flow. It is recommended that you use the client-server flow as described and demonstrated in the quick-start sample apps instead of using a server-side flow.
You can direct users to install the app at the conclusion of your install by linking to your app in the play store. From the play store, the user could still install your app directly to their device, it would just not happen in the sign-in dialog.