Identify which side of the existing rope is free from knots or snap hooks (the metal clasps to which you attach the flag), and, holding tightly to the rope, cut it.
Using your duct tape, tightly attach the new rope to the old (on the side that is free from clasps and knots) taking care to allow enough room that the rope can be threaded through the top of the pole.
Pull the rope through, taking care that the entire rope not be fed through. When finished, you should be holding the virgin end of the new rope, as well as the duct taped end that you have fed entirely through.
Cut the duct taped portion of the new rope off of the old rope (again, holding on to both ends of your new rope), and tie the two ends of the new rope together. Remove the snap hooks from the old rope and attach with spacing appropriate to the size of your flag.