You can use SWFLoader. Either place one inside your UIComponent, or if the MovieClip is the only thing inside the UIComponent, you can use the SWFLoader instead of the UIComponent.
Use the load method to load a SWF or an image, eg:
mySWFLoader.load("path/to/the/movie.swf");
If you don't want to load at runtime, you can embed the SWF in the Flex app instead. And in this case you only need an Image component with the source property set. eg:
<mx:Image id="myImage" source="@Embed(source='path/to/the/movie.swf')" />