Thanks for asking about that because it really should have been documented better. I just updated some of the information in the wiki to clarify how ANEs should be used in Visual Studio Code.
Basically, there are two places that you need to configure your ANEs. One for debugging and one for packaging.
For debugging AIR apps on your computer during development, you can set the
extdir field in launch.json to a directory containing your unpackaged/unzipped native extensions:
When packaging an AIR app to be installed on a device, you can set a different
extdir in the
airOptions section of asconfig.json to a directory that contains the actual .ane files: