Prepare barbecue (medium heat). Mix soy sauce, oil, 3 teaspoons ginger, and garlic in resealable plastic bag. Add flank steak and seal bag; turn to coat. Let stand at room temperature 30 minutes, turning occasionally.
Stir sugar and vinegar in small saucepan over medium heat until sugar dissolves; remove from heat. Add jalapeños and remaining 2 teaspoons ginger. Place cabbage and 1/2 cup green onions in medium bowl.
Pour vinegar mixture over and toss to coat. Season with salt and pepper. Let stand while grilling steak, tossing occasionally.
Grill steak until cooked to desired doneness, about 6 minutes per side for medium-rare. Transfer to work surface. Let rest 10 minutes. Slice steak thinly against grain. Sprinkle 1/4 cup green onions over slaw.
