Robert,
Technically the files are on the web server (which is loaded on the same machine as ArcGIS Server and ArcGIS Viewer for Flex Application Builder). However, I think (???) my hang-up may have something to do with not having the Web Adapter piece in place. Even without that piece in place I was able to systematically test some things as long as I was testing within our network. That is why I was confused when the Esearch function didn't work even though everything else (i.e. viewing the application as designed, seeing data with appropriate scale dependencies, identifying features with your Identify widget, etc.) seemed to work just fine. But I'm willing to concede that my problems might have something to do with the Web Adapter which is slated to be installed and configured next week. Perhaps I'll wait until then before losing any more sleep over this...
Thanks,
Sean