Alright, so the increased downwash caused by the trailing edge flap will increase the negative AOA of the tailplane and therefore the downward force of the tailplane which will result in a nose-up moment caused by the tailplane (if predominant over the nose-down moment caused by the flap extension).
However, lets assume we have a T-tail aircraft, where the horizontal tail is not in the downwash of the wing. Then I guess it will more likely be a pitch-down.
What I want to say. Itīs not possible to answer a question like "What pitch moment will occur on flap extension" as I wouldn't know which moments are predominant?