How do I make the Navigation Drawer of my Flutter app transparent?

I think there's a better way of doing this without messing up the entire canvases on the app. Since you want it specifically for the drawer, try this approach.

Scaffold(
   drawer: Theme(
      data: Theme.of(context).copyWith(
       // Set the transparency here
       canvasColor: Colors.transparent, //or any other color you want. e.g Colors.blue.withOpacity(0.5)
      ),
      child: Drawer(
          // All other codes goes here. 
       )
    )
 );

After much tinkering around I managed to find a solution. I edited the ThemeData and added a canvas color as described below

theme: new ThemeData(
   canvasColor: Colors.transparent
 ),

This isn't the best way to do this, it is more of a workaround than anything.

Visual Representation

use the transparent color like you are currently doing but also in the drawer widget use a stack and inside it make the first widget a backdropfilter, you will need to import dart:ui. here is an example

//import this library to use the gaussian blur background
import 'dart:ui';


Scaffold(
    appBar: AppBar(
        title: Text('Title'),
    ),
    drawer: Theme(
        data: Theme.of(context).copyWith(canvasColor: Colors.transparent),
        child: sideNav()),
        body: Text('Hello Body'),
),


Drawer sideNav(){
    return Drawer(
        child: Stack(
            children: <Widget> [
                //first child be the blur background
                BackdropFilter(
                    filter: ImageFilter.blur(sigmaX: 5.0, sigmaY: 5.0), //this is dependent on the import statment above
                    child: Container(
                        decoration: BoxDecoration(color: Color.grey.withOpacity(0.5))
                    )
                ),
                ListView(
                    padding: EdgeInsets.zero,
                    children: <Widget>[
                        DrawerHeader(
                            child: Text('Hello Drawer Title')
                        ),
                        ListTitle(
                            leading: Icon(Icons.dashboard, color: Colors.white)
                            title: "Dashboard"
                            onTap: (){

                            }
                        )
                    ]
                )
            ]
        )
    );
}