This thread on the Google Maps API for Flash Group Forum caught my attention yesterday:
The author outlines the steps required to get FlashDevelop up and running with the Google Maps API for Flash. FlashDevelop is a free and open source IDE with code completion for ActionScript, MXML, XML, and HTML.
It provides a compelling alternative to FlexBuilder and is worth a look. Please donate to the project if you use it!
I followed the steps outlined in the thread and everything worked as described. Here are a few extra details that might be useful:
Hope this helps!