For lubing the Reese Dual Cam, you only want to use a bit of Vasoline on the cams. That makes it silent on heavy hitch weight rigs.
As far as the chains go, all they do is hold up up the cam arms a they do not move at all so no need to lube there. The chains move some on the regular Reese hitch but not on the Dual Cam.
The rest of the hitch DOES need lubrication however. You should put oil or a bit of grease on the trunnion ends where they insert into the hitch head. If using a round bar hitch the ends of the bars where they insert should be heavily greased. Also the ball should have a coating of grease on it. You can download the instructions for the Strait-line hitch
here.Barney