Pat chicken wings dry, cut off and discard tips with a large heavy knife, and halve wings at joint. Stir together broth, soy sauce, cornstarch, and sugar in a small bowl until sugar is dissolved. Heat wok over high heat until a bead of water evaporates instantly. Pour in oil and swirl around side of wok to coat. Add chicken wings and pinch of salt and stir-fry, letting wings sit 5 to 10 seconds between stirs, until golden brown, 8 to 10 minutes. Add black beans, garlic, ginger, and red-pepper flakes and stir-fry 1 minute. Stir broth mixture, then add to wok, stirring to coat wings. Bring sauce to a boil, then reduce heat and simmer, covered, stirring occasionally, until wings are tender, about 15 minutes. Transfer to a shallow serving dish.