The cleanest way is usually to use a ViewStack. Depending on your requirements you may also be interested in using a TabNavigator or just a custom component as the "authenticatedView" of your primary ViewStack.
Fx 3 example:
<mx:ViewStack id="viewStack">
<mx:Canvas id="nonAuthenticatedView"/>
//Your login screen "stuff" can go here.
//On a successful login: viewStack.selectedIndex = 1.
//On logout set selectedIndex to 0 to return to the login screen.
</mx:Canvas>
<mx:Canvas id="authenticatedView">
//Instead of a Canvas this could be whatever, another ViewStack, TabNavigator, custom component, etc.
</mx:Canvas>
</mx:ViewStack>
This can get a lot more sophisticated if you start using a singleton model, bindings, and so on, but this should get you started.