I'm working on an application that connects to a php-mysql database in our server, instead of saving the result of the query in a file, you should save it (at least that is what I think so) in an internal Android Database (sqlite). There is a lot of information about databases in Android.
With this example you can see how to easily use sqlite and ContentProviders (a cleaner way of accessing data saved in your database.
In order to save correcty an JSONArray in your database i recommend you to use Jackson libraries in order to create objects from JSON making them easier to be saved.
Finally if the amount of information is relatively small you can use SharedPreferences aswell, this way the data can be accessed faster because it's saved in the mobile memory.
Hope it helps :)