Combine soy sauce, olive oil, lime juice, vinegar, garlic, salt, black pepper, white pepper, garlic powder, oregano, cayenne pepper, cumin, and paprika in a container. Place flank steak in the marinade and refrigerate for 8 to 24 hours.
Mix mango, avocado, lime juice, jalapeno, red onion, and cilantro together to make the salsa.
Set an oven rack at least 6 inches from the heat source and preheat the oven's broiler.
Remove flank steak from marinade and pat dry with paper towels.
Broil flank steak on high, flipping at the halfway mark, until steaks are beginning to firm and are hot and slightly pink in the center, about 18 minutes. An instant-read thermometer inserted into the center should read at least 130 degrees F (54 degrees C).
Cut flank steak into small cubes. Wrap 8 tortillas in a paper towel and heat in the microwave until soft, 20 to 30 seconds. Serve steak on tortillas.
