I am one of the users that is currently using ArcIMS to build a web GIS,so I have not had migrated to ArcGIS Server yet, therefore can I use Flex viewer 2.2 in ArcIMS 9.3 or 10? Will it cause any problem with it ? If so, can any one help me how to start learning with flex viewer for (API)?
Yes, you can use it. Here is ESRI's example: http://help.arcgis.com/en/webapi/flex/samples/index.html?sample=ArcIMS
You should look into the ArcIMSMapServiceLayer class: http://help.arcgis.com/en/webapi/flex/apiref/com/esri/ags/layers/ArcIMSMapServiceLayer.html