Updated method:
As of Dart Code (VS code extension) version 2.24.0, The 'Flutter: Inspect Widget' command was replaced with DevTools. (at the time of writing this, the latest version is 3.36.0. To get to the Inspect Widget from the command pallet with >Flutter: Open DevTools or >Dart: Open DevTools, requires several steps.
Here's a quicker way:
Click the debug (bug) button from the side menu and Select Run and Debug or press f5
The Widget inspector will open automatically.
Screenshot of emulator using the Flutter Widget inspector