The broccolini can marinate in the oil mixture for 8 hours, covered and refrigerated.
Prepare the barbecue for medium-high heat.
In a large bowl, whisk the oil, thyme, garlic, and chili flakes to mix well. Add the broccolini and toss to coat. Season to taste with salt and pepper.
Grill the broccolini until tender and lightly charred, turning as needed, about 8 minutes.
Transfer to a plate and serve.