It sounds like you're wondering about an OpenID "Sign in with Church Account" option, similar to "Sign in with Google" or "Sign in with Facebook" options that some websites and apps provide. Church Account supports OAuth with OpenID, but it's only available to Church-affiliated organizations like FamilySearch and BYU. Unfortunately, there's no authorized Church Account integration for third-party apps, as far as I'm aware.
Samuel Bradshaw • If you desire to serve God, you are called to the work.