There are two reasons we use thinner flaps (and elevators):
1. The thinner moveable surface prevents early airflow separation. If your flaps turn out too thick, they will disturb the air coming off the trailing edge of the wing. Then you will be trying to deflect turbulent air instead of smooth air. As Keith mentioned, your turns will be disappointing.
2. The thinner surface has a little "wiggle" room behind the trailing edge. This may be more noticable at the back of the plane, but it allows the surface to move around slightly before it intrudes into the airstream. The airplane will seem much more stable. My hand can shake without the airplane shaking, too. 
Remember that the air is flowing down the airfoil at the trailing edge of the typical NACA 0018 style airfoil and would come together at a certain spot behind the wing if we had no flap. If you taper the surface to approximate the airfoil, it will help.
There may be some other reasons, but these are the first that jumped into my mind. I hope the plane flies good for you.
Ron King