First edit your project's html-template/index.template.html file and add the following allowFullScreen property to the JavaScript code:
else if (hasRequestedVersion) {
AC_FL_RunContent(
...
"allowFullScreen","true",
...
);
AC_FL_RunContent(
...
"allowFullScreen","true",
...
);
You can also add the <param name="allowFullScreen" value="true"/> to the <object> tag, and allowFullScreen="true" to the <embed> tag for compatibility.
Next in your ActionScript code when the application has finished loading (when the stage isn't null) you can make your application full screen like this:
Application.application.stage.displayState = StageDisplayState.FULL_SCREEN;
I found this out from the The Adobe Flex 3 Programming ActionScript 3 PDF on page 547.