Usually, there will be an Icon button added to appbar when you add a drawer to the scaffold.
But when you have a custom appbar and you may need to add the button with on tap and below is the ontap code that helps you to open the Drawer.
Scaffold.of(context).openDrawer();
In my case, I added this button to an InkWell like below.
InkWell(
onTap: (){
Scaffold.of(context).openDrawer();
},
child: Icon(
Icons.menu,
size: appBarMenuIconSize,
),
),
Hope this helps. Thanks,
Srikanth