No legitimate method of unlocking Dark Kahn as a playable character has been discovered in any of the versions of Mortal Kombat vs. DC Universe. As the game was released in 2008, it is very unlikely that any method of playing as him exists.
In a 2010 interview, game designer Ed Boon confirmed that downloadable content had been planned for the game but had to be scrapped due to financial issues. New characters were planned, but Dark Kahn was not among them. The two characters of which Dark Kahn is a fusion, Shao Kahn and Darkseid, can be unlocked, however.