How have you configured Twonky to look for media? See the ‘Sharing’ page in the Twonky UI.
Can you play the duplicates, or does one of them fail?
What sort of media files are duplicated? All of them? One media type? Just a few files?
Are you using any backup system with the MyCloud, that might be genuinely duplicating files?
Do you have any other media servers on your home network?
There are a number of reports of DLNA file duplication; you might have a read of some of them:
http://community.wd.com/search?q=duplicate%20category%3A105
You might also benefit from careful configuration of the Twonky DLNA media server: