We've been using RiaTest http://www.riatest.com/ , and FlexMonkey http://code.google.com/p/flexmonkey/
(with various levels of success... we always got into some troubles in very specific cases).
However, for Flex like for any kind of GUI, I would suggest you try designing your code so that you can use pure flexunit tests to check most of your logic, before you go into "functionnal" testing in the browser.
Most of the time, I don't want to check that clicking on a button calls a function ; what I want is to test that the function works.
Hoping this helps.