I am building a cross-platform mobile app that interacts with a RESTful API, and I want to use OpenID Connect to authenticate my users. I will be building my own OpenID Connect
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.