What OpenID Connect authorization flow to authenticate mobile app users?

Mobile apps, at least on iOS and Android, can register custom URL schemes so that a redirect from a browser can send the user back to your app along with some query parameters.

So, you can use these flows in a native mobile app, but it involves sending the user to a web browser (either an external browser app or a web view built into your application) in order for them to authenticate with the OP.

A complete article presenting how to implement the "Authorization Code Grant" flow securely on a native mobile app is available here : Building an OpenID Connect flow for mobile. It is based on latest IETF OAuth 2.0 Security Best Current Practice.

Please also note that the use of the "Implicit Grant" flow is now highly discouraged.

I think that the Hybrid flow from the OpenID Connect spec is probably the one which you want to use. OpenID Connect Core Spec.

This does rely upon having a configured return URI, but as James says you would use a custom URI scheme to enable the mobile OS to redirect after login to your own app. Your app would then have an access code which it can use to obtain access tokens as needed (assuming that you are using Oauth2 to protect your back-end API services which the mobile app uses).

There is a vulnerability which would allow a malicious app to hijack your URI scheme and grab the tokens, There is a draft spec to overcome that Proof Key for Code Exchange by OAuth Public Clients which is worth considering implementing.