I love this question, because it highlights a key concept of subsonic aerodynamics.
It's common, but unfortunately incorrect, to think of the airflow as a linear flow from front to back. At subsonic speeds this just ain't the case. What happens at the back of the plane affects what happens at the front. You need to visualize the flow field and how it warps and twists around the object moving through the air.
I've spent some time with aero on race cars and it blew some of the engineer's minds to understand that what they were doing with the rear of the car affected what happened at the front of the car, but it does.
In it's simplest analysis the flap deflection changes the moment coefficient of the wing, and on a - let's say a flying wing config a downward flap deflection causes a downward pitching moment. With no horizontal stabilizer/elevator to add another moment in the opposite direction the wing will pitch in the direction of the flap deflection. The total pitching moment on the airplane is the sum of all the moments due to the wing, tail, landing gear, thrust, underwing stores, etc.
But - and it's a BIG but, it also alters the flow field around the ENTIRE airplane. On a conventional aircraft this may manifest itself as either a nose up OR nose down total moment on the plane with a free stick response as would be the case here.
Some airplanes pitch up when the flaps are deployed and some pitch down. It all depends on the total geometry of the and how the tail sits in the downwash of the wing.
As a general, and I mean really general rule with many exceptions - low wing planes will pitch nose down when the flaps are deployed, and conversely on high wings. But T-tails maybe not so much.
So, if you whack the fuselage off an Evolution or SV11 just aft of the flaps, the controls will reverse. Pretty easy to evaluate the moments due to lift there. Leave the tail on but disconnect the elevator and it's anybody's guess.
Probably not the answer you want but remember, we're talking about invisible flow fields that you need to visualize.
Navier-Stokes and Biot Savart ain't for sissies!
Chuck