Preheat grill for direct-heat cooking. Or position broiler rack so that top of meat on rack in pan is 3" from heat source; preheat broiler.
In pot, combine sugar, preserves, pineapple juice, lime juice, zest, garlic, and pepper flakes; over medium-high heat bring to a boil. Cook, stirring occasionally, until thickened, about 10 minutes. Remove from heat; cool.
Meanwhile, grill or broil chicken, turning once, 10 minutes per side. Brush chicken pieces with glaze. Continue grilling or broiling, turning once, until meat juices run clear when pierced with a fork, 7-10 minutes per side, brushing frequently with remaining glaze.