Here's what you should do:

In your Android Studio, go to File > Settings (Ctrl + Alt + S) > Language & Frameworks > Flutter > Tick to enable "Open Flutter Inspector view on app launch" > Click Apply, then OK.

After following the aforementioned instructions, the Flutter Inspector should be available every time you run it on an emulator or physical device.

Take note that restarting Android Studio is optional if changes are not applied immediately.

To see the related question thread: Flutter Widget Inspector - Not displaying