Heat oil and red pepper flakes in a skillet over medium heat. Add garlic, ginger, and scallion whites. Cook, stirring, until scallions are tender, about 1 minute. Add pork, breaking up with a spoon until cooked through, about 3 minutes. Add bok choy; cover and steam until tender, about 5 minutes. Remove from heat and add carrots. Season with vinegar and salt. Set aside.
Meanwhile, bring a pot of water to a boil. Season with salt. Add wonton wrappers one at a time. Cook until al dente, about 1 minute. Drain. Add wonton wrappers to skillet and toss. Serve with scallion greens.