The lathe method is good, but I have used a vise and a couple of pieces of copper or lead. Open the vise about 1", support the ends of the rod on the jaws on something soft (copper vise jaws, lead, or plastic) and rotate the rod tapping the high spot with a brass or lead hammer. You can also use the vise to do the straightening by setting up two support points on one jaw and a third pressure point on the opposite jaw. That allows the vise to be used to straighten the rod without pounding on it.
A plain flat surface won't work, since the rod has to be bent a tiny bit in the opposite direction so it can spring back to the right place, and a flat surface won't allow that.
FWIW, that rod is pretty strong and resistant to crushing but, as in many other situations, a light hand works best.
Jim