How do I set the background color of my main screen in Flutter?

You can set background color to All Scaffolds in application at once.

Just set scaffoldBackgroundColor: in ThemeData:

MaterialApp(
    title: 'Flutter Demo',
    theme: new ThemeData(scaffoldBackgroundColor: const Color(0xFFEFEFEF)),
    home: new MyHomePage(title: 'Flutter Demo Home Page'),
);