In a rectangular baking dish, combine the vinegar, mustard, garlic, salt, lemon juice and red pepper flakes and stir to combine. Slowly add the oil in a steady stream, whisking constantly. Add the rosemary sprigs. Place the skirt steak in the marinade. Cover and place in the fridge. Marinate for four hours (or overnight). Flip occasionally.
Remove the steak from the fridge about 30 minutes before cooking. Pat dry and set aside. Place the oven rack to the upper most level. Heat the broiler to 500 degrees.
Place the steak on a broiling pan and broil 6 minutes per side (for a medium doneness) for a total of 12 minutes. Remove from the oven, wrap in foil and let rest for 10 minutes. Cut the skirt steak in thin slices, against the grain.
While the steak broils, pour the marinade into a saucepan and reduce until the thickness coats the back of a spoon. Top the sliced steak with the marinade and serve immediately.