I suggest to not only store a boolean flag, but the complete version code. This way you can also query at the beginning if it is the first start in a new version. You can use this information to display a "Whats new" dialog, for example.
The following code should work from any android class that "is a context" (activities, services, ...). If you prefer to have it in a separate (POJO) class, you could consider using a "static context", as described [here][1] for example.
/**
* Distinguishes different kinds of app starts: <li>
* <ul>
* First start ever ({@link #FIRST_TIME})