Remember CL can be changed either by changing angle of attack or by changing the camber. (a couple of others as well, but as a pilot you can't directly control them)
As the question specifies straight and level flight and at a constant IAS then you have to generate the same lift, so CL must stay constant. Lowering the flaps will increase the camber (and in some aircraft the wing area as well) so the CL WILL increase. You have to keep the CL constant, so you will have to reduce the angle of attack to achieve that. The Cl increases when you extend flaps, BUT the question states that you are maintaining straight and level flight.. what do you have to do when you extend the flaps? You have to lower the nose to maintain level flight.. thus Cl remains the same..