If they're all SQL Server instances then you can create Linked Servers on the Destination server(s) to the Source server(s). Once you've done that, if the destination server is always the same then create a connection to it and amend the INSERT statement to include the server name as well for the source server.

If the destination will be on different servers then you can try changing the connection string using Expressions (you'll find this in the Properties against the connection you've created), but I haven't tried it with servers, so not sure if it will work.