I tend to use a combo of the Embed and SWC approaches. If you are bringing in animations as simple MovieClips then Embed will work just fine. If you want the objects you're embedding to have their own ActionScript (like the Flash UI components for example) then SWC is what you need.
Here's an overview of the swc approach:
Make sure you use the 'Export for ActionScript' option when you create your symbols in Flash, tick the 'export swc' option in the Publish settings and export it to your libs folder (where you've told your IDE to load SWC libraries from).
From then on you can create instances of the components and access their public properties or methods in your app. Say you've created a symbol called 'Screen', then you'd bring it into your Mediator simply by doing 'var screen:Screen = new Screen()'.
Easy