Lets suppose I've asked a question on Super User. After a few days there were little or no responses to my question. After those few days I also realized that maybe the question would fit better if asked on Serverfault. Is there a way to flag the question / contact the moderator directly and ask him for a permission to move the question to other stack exchange site?
Use the Flag -> Other option and ask for it to be migrated to $site. It might be worth asking in the target $site's chat room if it would be a good fit beforehand.