I recently worked on a Flex mobile project where the mobile app was required to sit on browser as well.
There is no official way of converting the flex mobile project into a flex web application right from within the Flash Builder. I used this post to get the ball rolling http://www.riagora.com/2011/08/flex-mobile-in-the-browser/ I managed to get my mobile app working on browser but..
As I navigated away from the home screen I started getting run-time errors for StageText. I immediately noticed that I had spark TextInput and TextArea on the view. I took them out and everything was fine again. Changed them to mx for a minute and it was fine with that too but it just won’t like me using spark TextInput and TextArea. Since I had changed the theme to be mobile theme for this app (one of the required steps of the initial setup), I thought that might be forcing the spark TextInput/TextArea instances to use StageText. I changed the skins for TextInput and TextArea to use spark skins rather than the default (mobile in this case) and it worked fine.
As you can see in the video I keep getting compiler errors which I got rid of by cleaning the project a couple of times but I wasn’t sure what was the cause. I used Flex 4.6 SDK with AIR 3.3.