You can add additional levels of detail (lod's) to the configuration, which will allow you to zoom 'beyond' the available levels of the cached base map. From the Flex Viewer help - look for the tag in the 'Map content' section toward the bottom of the page :
http://help.arcgis.com/en/webapps/flexviewer/help/index.html#/Main_configuration_file/01m300000018000000/
Here is a sample from a modified Flex Viewer:
<lods>
<!--Custom levels specified to get 'below' the Esri basemaps-->
<lod resolution="76.4370282850732" scale="288895.277144"/><!-- 11 -->
<lod resolution="38.2185141425366" scale="144447.638572"/><!-- 12 -->
<lod resolution="19.1092570712683" scale="72223.819286"/><!-- 13 -->
<lod resolution="9.55462853563415" scale="36111.909643"/><!-- 14 -->
<lod resolution="4.77731426794937" scale="18055.954822"/><!-- 15 -->
<lod resolution="2.38865713397468" scale="9027.977411"/><!-- 16 -->
<lod resolution="1.19432856685505" scale="4513.988705"/><!-- 17 -->
<lod resolution="0.597164283559817" scale="2256.994353"/><!-- 18 -->
<lod resolution="0.298582141647617" scale="1128.497176"/><!-- 19 -->
<lod resolution="0.1492910708238085" scale="564.248588"/><!-- Custom1 -->
<lod resolution="0.0746455354119043" scale="282.124294"/><!-- Custom2 -->
<lod resolution="0.0373227677059522" scale="141.062147"/><!-- Custom3 -->
</lods>