ArcGIS Online 3.6 contains a new basemap, US Geological Survey (USGS) National Map layer, which is hosted on a site with the locked down clientaccesspolicy.xml and crossdomainpolicy.xml files.
This returns a channel security error when trying to use the ArcGIS Online basemap switcher within ArcGIS Viewer for Flex and ArcGIS Viewer for Silverlight applications, which are hosted on a domain where the domain is not whitelisted in the abovementioned files.
Disable the use of the ArcGIS Online basemap gallery within ArcGIS Viewer for Flex and ArcGIS Viewer for Silverlight applications, and manually add basemaps except USGS basemap.In ArcGIS Viewer for Flex application, uncheck the Add Portal for ArcGIS Basemaps checkbox when ArcGIS Online is set as portal URL in the Advanced Settings.