Back again. I asked it to WPML support theme and they refer to you, the theme builders. See below what they say:
Hi,
this demo site is also ok. But code which you privded is only to display menu under current language and dont include this current language.
But this is a part of theme (you can switch to standard wordpress theme nd you will see that it works as expected) so I am affraid that I have to refer you again to theme authors 🙂 But I will give you some code which you can show for them, and then they will be able to fix this.
To display flag of current language, here is a snippet:
http://pastebin.com/VfTTFfKR
They should put this code in their theme in place where flag should be displayed
Please let me know if you are satisfied with my answer and if I can help you with any other questions you might have