First be careful with the divergence theorem as the cone is not closed and so the divergence theorem does not apply. Note however that the value of the vector field on the flat surface is zero so it wont contribute to the flux and you can close the surface and then apply the divergence theorem.

My guess is that you having problems parameterizing this becuase it is not centered at the origin. We can fix that by shifting everything down 6 units

This gives the equivilent problem

S for

and the vectorfield is

Now the parametric form of the cone can be found using Cylindrical coordinates or spherical coordinates.