In a large, heavy skillet over high, heat 2 tbsp. oil. Add steak and salt and cook, stirring frequently, until browned, about 5 minutes. Transfer to a plate.
Add remaining 1 tbsp. oil to skillet, reduce heat to medium-high, then add ginger and garlic, and cook for 30 seconds. Add celery, green onion, carrot and pepper flakes, and cook, stirring frequently, until crisp-tender, about 4 minutes. Stir in steak, tamari and sesame oil, and toss together.
In a large, dry skillet over medium, heat tortillas one at a time, flipping once, until heated through and pliable. Transfer to a plate and warm remaining tortillas, stacking them on top of each other.
To serve, top each tortilla with a lettuce leaf, and fill with steak and vegetable mixture. Top with green onion and sesame seeds.