How to change shadow color of AppBar?

There isn't a way to change the colour of the default shadow but you can get around it by wrapping your AppBar in a Container which is inside a PreferredSize widget:

void main() => runApp(App());

class App extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      home: Scaffold(
        appBar: PreferredSize(
          child: Container(
            decoration: BoxDecoration(boxShadow: [
              BoxShadow(
                color: Colors.red,
                offset: Offset(0, 2.0),
                blurRadius: 4.0,
              )
            ]),
            child: AppBar(
              elevation: 0.0,
              title: Text("Test"),
            ),
          ),
          preferredSize: Size.fromHeight(kToolbarHeight),
        ),
        body: Container(),
      ),
    );
  }
}