Update ArcGIS Online webmap in ArcMap 10.1?

[Gyeong_MinRoh]

Hello.

I'm making web applications from ArcGIS Online Web Map using ArcGIS Viewer for Flex.
These applications are going to be embedded to my company's website for internal use.
If I'm not wrong, Flex Viewer seems to support only Web Maps or operational layers in application builder.
(We can't add Map Service that has been shared from ArcMap 10.1)

I would like to ask if the Web Map can be edited and updated from ArcMap 10.1?
(I found out that ArcMap 10.1 can open the Web Map from ArcGIS Online
but it seemed that there's no way to synchronize this map to ArcGIS Online which had been edited to ArcMap 10.1.)

I think it will save much time and provide more functionalities.
But if not, I will still continue to edit with the default ArcGIS Online Map Viewer anyway.

Many thanks.

[JonathanQuinn]

You mention that "We can't add Map Service that has been shared from ArcMap 10.1".  Did you create hosted feature services that are on ArcGIS.com in an organization?  First, make sure that your hosted feature service is editable within the properties on ArcGIS.com.  Next, you can sign in to ArCGIS.com using your organization account in the Flex Builder application and then add your feature services.  In the Edit widget, your feature service should be listed as editable.  Any changes will be synced automatically to the hosted feature service, (you can make edits in the Flex application and then open up the feature service in the ArcGIS.com Map Viewer to see the changes).