There seems to be no API that helps on iOS/Android retrieve local media files.
It would be nice if this could be made available.
For iOS this could use the following built-in API : https://developer.apple.com/library/ios/documentation/Audio/Conceptual/iPodLibraryAccess_Guide/UsingtheMediaItemPicker/UsingtheMediaItemPicker.html
While for Android, it would be based on :
http://developer.android.com/reference/android/provider/MediaStore.html and using query such as the one in this example :
Android does not provide a nice UI such as the one provided by iOS so it is up to the developer to provide such UI.