Using DateList first and then using DateObject seems to work:

DateObject[
 DateList[{"2014/01/09 07:24:36:985", {"Year", "/", "Month", "/", 
 "Day", " ", "Hour24", ":", "Minute", ":", "Second", ":", 
 "Millisecond"}}]]

But still no fractional seconds. As previous comment suggests I guess it's not supported.