It's an old question. But for those who come across this question...
The white background behind the rounded corners is not actually the container. That is the canvas color of the app.
TO FIX: Change the canvas color of your app to Colors.transparent
Example:
return new MaterialApp(
title: 'My App',
theme: new ThemeData(
primarySwatch: Colors.green,
canvasColor: Colors.transparent, //----Change to this------------
accentColor: Colors.blue,
),
home: new HomeScreen(),
);