For there to be only one reflection symmetry, the 2D polygon has to have one line of symmetry but no others, so maybe something like a Christmas tree or arrowhead shape. But the problem is that then there are no nontrivial rotational symmetries. If I consider a line segment, then there is only one reflection, but it is identical to a rotation in that case.
It seems impossible to have exactly one reflection and 1 or more rotations in 2D, but how could I prove that? Or maybe I am mistaken and it IS possible?