Just ran into this issue myself (again).
As pointed out by @TirthPatel (see comments), there is a Flutter suggested way of opening the project via Android Studio, see here, i.e.
Which file do I open?
Via Welcome Screen or File > Open, select the build.gradle file located in /path-to-plugin/example/android/gradle.build
No libraries/modules shown except app
This is a precautionary set of steps, one that I haven't resolved to a single action to address the problem.
You may find .idea folders, and .dart-tool.
.idea contains IDE specific configurations, etc (see this or this for some more info, though not specific for Android Studio)
.dart-tool contains dart related configurations and pre-build files (via build-runner, locales via i18n, etc. (see here or here for more info)
Note: these can be/are generated
I deleted .idea and .dart-tool folders in
/path-to-plugin/
/path-to-plugin/android
/path-to-plugin/example
/path-to-plugin/example/android