Prepare a medium-hot fire for both direct and indirect cooking in a charcoal grill with a cover, or preheat a gas grill to medium-high. If using charcoal, the coals should be placed so that they are under half of the rack, creating 2 zones: 1 hot and 1 mildly hot. If using a gas grill, follow manufacturer's instructions to create zones for both direct and indirect grilling. When the grill is hot, clean it with a wire brush. It does not need to be oiled at this time.
To make the honey plum sauce, combine the plums, honey, garlic, ginger, rice wine vinegar, hoisin sauce, and dried pepper flakes in a fireproof saucepan and place on the grill over medium-high heat. Bring to a boil and then place the saucepan to the side of the grill with indirect heat and simmer, covered, for 15 to 30 minutes, until the plums are completely cooked. Place the mixture in the bowl of a food processor or blender and puree until well combined. Season, to taste, with salt and pepper. Add more of any specific ingredient you feel necessary (e.g., honey, hoisin sauce).
To make the patties, remove the skin from the duck breasts. Place the duck breasts and 1 of the skins in the bowl of a food processor and pulse until well combined. Transfer the duck mixture to a large bowl. Add scallions, cilantro, five-spice powder, salt and pepper to the bowl. Handling the meat as little as possible to avoid compacting it, mix well. Divide the mixture into 6 equal portions and form the portions into patties to fit the onion rolls.
Brush the grill rack with vegetable oil. Place the patties on the rack, cover, and cook, turning once, just until done, about 3 minutes on each side. During the last few minutes of cooking, place the onion rolls, cut side down, on the outer edges of the rack to toast lightly.
To assemble the burgers, place a generous amount of the honey plum sauce on the cut side of the onion rolls. On the onion roll bottoms, place a patty and an equal amount of napa cabbage. Add the onion roll tops and serve.