Bring a large pot of salted water to a boil over medium-high heat. Add the broccoli and blanch until it turns bright green, then remove to a large bowl of ice water to shock and to stop the cooking. Drain the broccoli and dry well with paper towels. Put the broccoli into a large resealable plastic bag.
Whisk the olive oil, red pepper flakes, Neely's Dry Rub, white wine vinegar, salt, pepper, and garlic together in a small bowl. Pour over the broccoli and seal the bag. Let marinate for 30 minutes.
Preheat the grill to medium heat.
Remove the broccoli from the bag, letting the excess marinade drip off. Put on the grill and cook until lightly browned and fork tender, about 4 minutes. Transfer the broccoli from the grill to a serving platter and serve.