Have you thought of using Application Builder? It allows you to choose multiple custom or ArcGIS Online basemaps for use in the application. Here are the [instructions][1] on how to do that. After you have build your application, you basically deploy a Flex Viewer application at your web server. If you still prefer to use the source code of Flex Viewer and do all the development on your own, then look for the [tag reference here][2] which will help you to set additional basemaps in your configuration file.

Open config.xml and edit the basemaps tag:

    <basemaps>
    <layer label="CustomBaseMap"    type="tiled" visible="true"
                           url="http://server/ArcGIS/rest/services/BaseMaps/BaseMap/MapServer"/>
    </basemaps>

  [1]: http://resources.arcgis.com/en/help/flex-viewer/concepts/index.html#/Maps_tab/01m300000041000000/
  [2]: http://resources.arcgis.com/en/help/flex-viewer/concepts/index.html#/Map_content/01m30000005p000000/