How do I install a flutter in VS code with an emulator without Android Studio?

Right now, installing Android Studio is the supported way to get all the bits you need:

https://flutter.io/setup-windows/#system-requirements

Flutter relies on a full installation of Android Studio to supply its Android platform dependencies. However, you can write your Flutter apps in a number of editors; a later step will discuss that.

It is possible to make things work without (by installing bits of the SDK, Gradle, etc. manually, and ensuring they're on PATH or in relevant env variables) but it's more complicated. I (the author of the Dart/Flutter VS Code plugins) used to run without Android Studio but things like upgrading the Android SDK are much simpler with Android Studio (as far as I can tell, the GUI for updating the SDK was seemingly moved from the SDK into Android Studio).