This option would accomplish that.
"dart.devToolsLocation": "external"
Answer from Ramin Mousavi on Stack Overflowflutter - Get Dart Devtools to open in Chrome - Stack Overflow
Cannot open dev tools in flutter web --profile
dart - Flutter in VSCode is not connecting to devtools - Stack Overflow
Flutter Inspector in Visual Studio code - Stack Overflow
Videos
Update VSCode to the newest Version.
VSCode Update
Update Flutter
flutter Update
Now run your Project and then click [ctrl] + [alt] + [d] for running dart devtools. VSCode is asking you where you wish to open DevTools.

Do not bother about it mate, just add this line on settings.json
"dart.embedDevTools": false
Then you will get again DevTools on Chrome. Just shortcode: Ctrl + Alt + D.
That's it.
Starting with version 2.24.0 the DevTools option is the new feature for debugging and inspecting.
Open the command palette Ctrl+Shift+P and type:
>Dart: Open DevTools
To access it your debug session must be running:

as Danny Tuppeny (the creator of the dart plugin in VScode) mentioned :
the Flutter Inspector is not currently available in VS Code
you can follow this issue for more updates
UPDATE :
In the new Dart Code plugin for VS Code there is something similar, look here
