As stated above, Cityjet is not a Skyteam member. Therefore, the KL code is only half the story. The entire flight has to be Skyteam (coded and operated) in order to earn Millemiglia miles.
There is a daily (except Sundays) Alitalia flight from FCO to LCY and back; AZ212 departs Rome at 09:00, arriving at 10:25; AZ211 departs City at 10:55, arriving back in Rome at 14:25.