I have installed Flutter on Windows and checked all is ok using flutter doctor. I imported the Flutter plugin.
Now, when I try to create a new Flutter app via Anroid
This is likely because you've put Flutter in Program Files which requires admin permissions to be able to write its cache files.
Program Files
I've got a PR Open that should result in a more friendly error, but I'd recommend moving Flutter away to a folder that non-Admin users can write to.