JVESoft has a native platform persistent storage component as part of their JVESoft Component Suite for Delphi XE8 Firemonkey. The component wraps the API for accessing the Registry on Windows, JSharedPreferences on Android, and NSUserDefaults on IOS and Mac into a single cross platform API. You get access to standard functions like WriteBool, WriteString, WriteInteger, WriteDate, WriteDateTime, WriteFloat, WriteTime, ReadBool, ReadString, ReadInteger, ReadDate, ReadDateTime, ReadFloat, ReadTime, and DeleteKey. There is a similar component that is free which handles only Windows and Android. And similar free libraries here and here which also wrap the various native platform storage APIs too. Personally I prefer to just use TIniFile or an SQLite database but there may be some cases where using the native platform APIs to store your app settings can be beneficial. The JVESoft suite is a commercial product and there is no free trial. There are quite a few other components in the component suite as well which you can read about here, here, and here. It should also work in Appmethod.
FMXExpress.com has over 700 tips and tricks for building cross platform apps on Android, IOS, OSX, Windows, and Linux with a single codebase and single UI using the FireMonkey framework found in Delphi and C++Builder.
FMXExpress covers top cross platform secrets for FireMonkey in C++Builder and Delphi XE5, XE6, XE7, XE8, Seattle, Berlin, Tokyo, Rio, and Sydney.