If you already have the normal vector, you're almost there. What you now need is the angle (look for dot product) between the normal and a vertical line (what exactly vertical means depends on your application).
If your normal vectors are actually normalized (have length 1) and the vertical is (0 0 1), the cosine of the slope angle is simply the z coordinate of the normal vector.
To demonstrate this: Take a pen and let it stand on your table. This is your table's normal vector. The angle between this vector and a vertical line is zero, as your table has no slope at all. If you tilt your table by a certain amount, the angle between the normal and a vertical line will increase by the same amount.