Use nothing less than 20 pound test and 25 to 30 pound goat rope is even better. Lighter lines can and will work, but you'd better own a tackle shop to keep yourself supplied. Not to mention the deep pockets you'll need to pay for the stuff. Dodgers present a special problem because for the sideways turn and floppy roll. When a large King takes the snap out of a dodger I've seen 20 pound test break at the release from the force of the hit.
Heavy line is needed handle the heavy hitters, like Kings.
When trolling any type attractor stiffen up the down rigger releases because of the added drag and you'll hook up on more fish. Kings as a rule prefer a longer lead length of 18 inches or more behind a size 0 dodger, Cohos like a faster fly on a shorter leader. A double overhand loop is the knot you tie to attach the fly, squid or bait to a dodger, cowbell or flasher. Double the line, then tie a double granny knot and your there. Use a good quality leader on your flies or squids.