Combine soy sauce, teriyaki sauce, and next 4 ingredients in a large zip-top plastic freezer bag or shallow dish. Add steak, and turn to coat. Seal or cover, and chill 4 hours, turning occasionally.
Remove steak from marinade, discarding marinade.
Grill flank steak, covered with grill lid, over medium-high heat (350° to 400°) 5 to 7 minutes on each side or to desired degree of doneness. Let stand 10 minutes before slicing. Cut diagonally across the grain into thin strips.