Rub the chicken with vegetable oil, allspice, thyme, garlic powder, cayenne and salt and refrigerate for 30 minutes to 4 hours.
Toss the cabbage and mango with lime juice and mayonnaise and refrigerate the slaw.
Heat a grill or grill pan to medium-high and cook the chicken for 5 to 7 minutes per side, until dark at the edges and 165°F inside.
Rest the thighs for 5 minutes while toasting the buns cut-side down for 1 minute.
Stir the slaw once more and drain off any liquid collected in the bottom of the bowl.
Place 1 grilled thigh on each bun and top with 3/4 cup mango-cabbage slaw.