Thank you for your question. Using the AGSClosestFaciltyTask is very similar to the other task-based APIs, such as the AGSRouteTask (routing) or the AGSLocatorTask (geocoding). Samples for those can be found in the ArcGIS Runtime Samples app for iOS: GitHub - Esri/arcgis-runtime-samples-ios: Swift samples demonstrating various capabilities of ArcGIS...
Specifically, for routing:
And for geocoding:
If those don't help, please post the code you're having problems with and I'll take a look.