There are several things going on when you extend trailing edge flaps ---
1. You're increasing the lift due to increase in wing area and geometry. This results in a balloon. The C-17 deploys spoilers when extending flaps as anti-ballooning action. The change in geometry can be visualized as both a change in chamber, which results in an instantaneous increase in local angle of attack, as well as different lift characteristics (CL, CD, & CM_alpha vs alpha).
2. You're increasing the down wash on the horizontal stabilizer, resulting in a pitch down.
3. Anytime you change the span wise lift distribution on a swept wing, you get a pitch change. The manufacturer tries to minimize this by careful placement of the trailing edge flaps. Some aircraft (B707, B747), you can split the outboard and inboard trailing edge flaps and extend one set to affect a change in pitch.