The quick answer is, sadly, NO you can't use google maps in flex application. The next thing i thought a bit is that if it wasn't illegal ESRI programmers would implement google maps in ArcGIS Viewer for Flex - it's not hard to get these maps in Flex app thanks to Javascript function. Google does not longer supports Flash developers - you can't get new Google Maps API key for Flash, only Javascript developers are welcome.
Hope this helps. If you'll find something that deny what I've said please let me know!
Thank you Marcin - very good of you to dig these up. I had found the first post but not the second - like you said, seems to be a resounding no. I'll post back here if I find a solution to this.