The real problem is that you are using dynamic return type in the FacebookClient Get method. And although you use a method for serializing, the JSON converter cannot deserialize this Object after that.
Use insted of:
dynamic result = client.Get("fql", new { q = "select target_id,target_type from connection where source_id = me()"});
string jsonstring = JsonConvert.SerializeObject(result);
something like that:
string result = client.Get("fql", new { q = "select target_id,target_type from connection where source_id = me()"}).ToString();
Then you can use DeserializeObject method:
var datalist = JsonConvert.DeserializeObject<List<RootObject>>(result);
Hope this helps.