In a food processor, whirl the parsley and garlic until finely chopped. With machine running, add oil, vinegar and 1 tablespoon water in a steady stream. Season with red pepper flakes, 1/2 teaspoon salt and 1/2 teaspoon pepper. Pour about half of the chimichurri into a small bowl.
Prepare grill. Season cubed beef with 1/4 teaspoon salt and 1/8 teaspoon pepper. Thread beef and chorizo pieces alternately onto skewers. Brush meat with the chimichurri sauce left in food processor.
Grill skewers over direct high heat, with the lid closed as much as possible, until steak is cooked to your desired doneness, 4 to 6 minutes for medium-rare, turning 2 to 3 times (watch for flare-ups). Serve warm with the reserved chimichurri spooned over the top.