@Antoine Basically you can set your theme Brightness, or you can manually override the appbar brightness using the following :

appBar: new AppBar(
  title: new Text(widget.title),
  brightness: Brightness.light, // or use Brightness.dark
),
Do note that this will only switch between white and black status text color.

.dark will make the status bar text WHITE, while .light will make the status bar text BLACK

Maybe for a more custom color, like the comment said you can view SystemChrome class.