Flex and Flash is a great tool for enterprise level applications.
Our general rule of thumb is to use Flex or Flash when the type of rich interface required cannot be achieved using html/javascript/ajax. In this event the rich UI in flash/flex should be built keeping in mind that its the "Presentation Layer" and apart from basic front-end validation all the work (server side validation and logic) should be done by the underlying application. I would say that flex/flash should be used ot build component parts of an interface, not the whole interface.
The advantages are mainly in achieving a much richer and more stable interface than html/javascript/ajax type interfaces. In my experience the development time may not neccessarily be quicker, but the end result can be much greater!
The disadvantages I have experienced come in the form of finding the right kind of developers and finding developers to take over projects if contractors are used.