When updating text via data binding in Flex, JAWS (or other screen readers) will not automatically read the change. Imagine a Flex application where every time a visual String was updated, the screen reader read that change. It would be worse than being in a theatre before the curtain rises! However, after data binding has occurred, you can use your screen reader shortcuts to move back and forth through the accessible properties and hear any changes that have been made.
The best way to review what text should be read is to use an accessibility inspector such as Inspect32, or Accessibility Explorer (both available from Microsoft). You can step through the MSAA properties and review the descriptions and names. I find the easiest way to ensure you’re looking at just Flash Player is to use Accessibility Explorer and use the select with mouse tool and click on an instance of Flash Player within a browser.