After reading this FlexUnit tutorial:
I downloaded the files here:
...and changed the project, FlexUnit4Examples, to an AIR application via FlashBuilder. After I did that, it no longer passes all of its asynchronous tests.
Do asynchronous tests have any issues or limitations with AIR?
The problem I had was not related to FlexUnit. It was the way I was tried to access the file system when it was an AIR application. I used FileStream instead of what was in the tutorial that worked with a web base application, which was HTTPService.
Since I am new with unit testing, I assumed that it was the test that was coded wrong. I suppose I havent trusted my unit tests enough, since it told me that my source code was incorrect.