Combine first 10 ingredients. Reserve 1/3 cup red wine mixture.
Place flank steak in a large shallow dish or a large heavy-duty zip-top plastic bag. Pour red wine mixture over steak. Cover or seal, and chill 2 to 4 hours, turning occasionally.
Remove flank steak from marinade, discarding marinade.
Grill, covered with grill lid, over medium-high heat (350° to 400°) for 8 to 10 minutes on each side or to desired degree of doneness, brushing with reserved wine mixture using rosemary sprigs. Cut steak diagonally across the grain into thin strips. Squeeze juice over steak before serving.