I'm a Java developer at heart and love my Eclipse and Android Studio/IntelliJ IDE's.  That said I am always open to trying new tools and although it would pain me a few years back to install Microsoft products I feel the tide has turned, MS changed their ways over that time and embraced the open source community - a do or die tactic in my opinion, luckily they chose the 'do' option, anyway I drift off topic.  I found Microsoft's Visual Code works really well with the whole Flutter tool set so follow these steps below to get up and running:

• Download Microsoft Visual Code IDE
• Download and install Android Studio - provides tools necessary for developing Android apps
• If you intend to deploy on iOS then you'll need Xcode
• Head to flutter.dev and download the right OS version, follow installation instructions for your chosen OS
• Fire up MS Visual code and install the following plugins:
  • flutter - Flutter support and debugger for Visual Studio Code
  • dart - Dart language support and debugger for Visual Studio Code
  • awesome Flutter Snippets - a collection snippets and shortcuts for commonly used Flutter functions and classes

That's it, you're all set up to write your million dollar cross-mobile app!