UPDATE:
Well, miraculously I've been able to get the Navigation widget to appear in my "straight" Flex API application. None of the skins are applying for some reason, but I think I can figure that one out on my own. The reason I'm writing again is to get some ideas about another problem I'm facing...
Even though the widget appears on the interface, not all of the functionality is working. The pan arrows and the zoom slider themselves work, but the full extent, previous extent, and pan, zoom in, and zoom out button bar are all broken. I only changed code in the NavigationWidget.mxml file, but something I did must have broken something. To give you an idea of what I did, I deleted:
import com.esri.viewer.AppEvent;
import com.esri.viewer.ViewerContainer;
and the init and sharedDataUpdated functions. I was uncomfortable about deleting the init function, but if I don't, the app won't run at all.
Anyhow, the error I get when I click on the full extent button reads:
"TypeError: Error #1009: Cannot access a property or method of a null object reference.
at widgets.Navigation::Navigation/__innerButton_click()"
So I'm halfway there. If you have any other thoughts, Bjorn (or anyone else), I'm all ears.
Thanks again,
Justin