Bring vinegar to a boil with sugar, red-pepper flakes, 2 tsp salt, and 1 Tbsp pepper in a small nonreactive saucepan, stirring until sugar has dissolved, then cool. Set aside 2 cups vinegar sauce to serve with sandwiches.
While sauce cools, score pork skin in a crosshatch pattern with a sharp knife (forming 1-inch diamonds), cutting through skin and fat but not into meat. Pat meat dry and rub all over with 1 Tbsp each of salt and pepper.
Let stand at room temperature 1 hour before grilling.
Prepare grill for indirect-heat cooking over low heat, leaving space in middle for disposable roasting pan.
When coals have cooled to about 300°F (45 minutes to 1 hour; when most coals will have burned out), put disposable roasting pan on bottom rack of grill between the 2 remaining mounds of coals, then fill pan halfway with water.
Add a couple of handfuls of unlit charcoal to each charcoal mound, then put grill rack on so hinges are over coals.
Oil grill rack, then put pork, skin side up, on rack above roasting pan. Grill pork, with lid ajar (for air, so coals remain lit), basting meat with sauce and turning over every 30 minutes (to maintain a temperature of 250 to 275°F, add a couple of handfuls of coals to each side about every 30 minutes), until fork-tender (a meat fork should insert easily) and an instant-read thermometer inserted 2 inches into center of meat (avoid bone) registers 190°F, 7 to 8 hours total.
Transfer pork to a cutting board. If skin is not crisp, cut it off with at least 1/4 inch fat attached (cut any large pieces into bite-size ones) and roast, fat side down, in a 4-sided sheet pan in a 350°F oven until crisp, 15 to 20 minutes.
When meat is cool enough to handle, shred it using 2 forks.
Transfer to a bowl.
Serve pork, cracklings, and coleslaw together on buns.
Serve reserved vinegar sauce on the side.
Pork can be roasted in a large roasting pan, covered with parchment paper and then foil, in middle of a 350°F oven. Roast 1 hour, then pour 1 cup vinegar sauce over meat. Roast 1 hour more, then baste with 1 cup more sauce. Continue to roast, covered, adding water (1/2 cup at a time) to pan if needed, until fork-tender (a meat fork should insert easily), about 2 hours more.
Cut off skin (see recipe above) and roast in a 4-sided sheet pan on lowest rack of oven. Meanwhile, return pork to oven and roast, uncovered, on middle rack, until meat is browned and skin is crisp, about 45 minutes more (5 to 6 hours total roasting time, depending on size of roast).
