Bring large pot of salted water to boil over medium-high heat. Add broccoli and blanch until it turns bright green, remove to large bowl of ice water. Drain broccoli and dry well. Place broccoli in large resealable plastic bag.
Whisk olive oil, red pepper flakes, dry rub, salt, pepper, and garlic together in small bowl. Pour over broccoli and seal bag. Let marinate for 30 minutes.
Preheat grill to medium heat.
Remove broccoli from bag, letting excess marinade drip off. Put on grill and cook until lightly browned and fork tender, about 2-4 minutes each side.
Transfer broccoli from grill to serving platter, spinkle with vinegar and serve.