I believe that is just something that JAWS does with long chunks of text. It pauses after a while for some reason - to let the listener catch up? I'm not exactly sure. There is a keystroke to continue reading once it pauses, however (down arrow?).
I don't think this is specific to a Flex TextArea - you should be able to reproduce the behaviour with a long chunk of text on a web page. IIRC, there are JAWS keyboard commands to read the whole page without stopping, which users of your app could use if that is what they wanted to do.
In general, this sort of behaviour is hard (impossible) to change. Here's why:
Flash and JAWS communicate through the Microsoft Active Accessibility interface. Through this interface, Flash provides JAWS (or any other screen reader) a tree of objects. Each object has a role (checkbox, textarea, etc) and a limited set of other properties (whether the checkbox is checked, the text in the textarea, etc).
Once JAWS reads the text of your textarea through this interface, it is free to process and read that text in whatever way it wishes, including inserting pauses. There is nothing you can do as a Flash developer to reach through this interface and say "please read all this text without stopping".