Hi
When I look at the rest endpoint for the Wildfire feature service:
http://services.arcgis.com/P3ePLMYs2RVChkJx/arcgis/rest/services/Wildfire/FeatureServer
And scroll all the way to the bottom, I can see the Sync and Replica Operations are available:
Supported Operations: Query Apply Edits Create Replica Synchronize Replica Unregister Replica
The other feature services you mention only show Query and Apply Edits.
Supported Operations: Query Apply Edits
Please have a look at this Guide topic Create and Offline map:
https://developers.arcgis.com/android/guide/create-an-offline-map.htm
One of its topics describes 'a sync-enabled feature service' and creating one.
Please let me know if this helps get you any closer to solving the issue.