Combine the soy sauce, vinegar, scallions, sugar, ginger, sesame oil, and pepper flakes in a bowl. Whisk well to blend. Reserve 1/4 cup and set aside. Pour the rest into a plastic bag with a resealable closure. Add the skirt steak and seal. Marinate in the refrigerator, turning the bag often, for at least 4 hours or overnight.
Fill a large deep saucepan to a depth of about 2 inches with vegetable oil. Heat over medium-high heat until a deep-fat thermometer reads 375 degrees F. (Alternatively, use an electric deep-fat fryer) Pull apart the clusters of noodles into clumps of about 10 strands each. Working in batches, fry the noodles, turning once, until they puff up and turn white, about 10 seconds. Use a slotted spoon or a spider (a slotted spoon designed like a spider's web used for deep-frying) to transfer to paper towels to drain.
Remove the skirt steak from the marinade and pat dry with paper towels. (The drier the beef, the better it will sear.) Working in batches, heat half the oil in a large skillet over high heat until almost smoking. Season the meat with salt and pepper. Place in the skillet and reduce the heat to medium-high. Cook until seared on the outside and rare to medium-rare on the inside, 2 to 3 minutes per side. Transfer to a platter, cover loosely with foil, and let rest for 5 minutes. Repeat with the remaining oil and skirt steak. Cut into very thin slices, holding the knife at an angle and cutting against the grain. Toss with the reserved 1/4 cup sauce in a large bowl until well coated.
Crumble the fried noodles and mound on individual serving plates. Top with equal portions of the beef and garnish with chopped scallions.