In a large saucepan, heat oil over medium-high heat. Add chicken, skin side down, and cook until skin is golden and crisp, about 5 minutes. Flip and cook 2 minutes more. Transfer chicken to a plate. (May need to do this in batches, depending on the size of your saucepan.).
Discard all but 1 tablespoon fat from pan. Add garlic and cook, stirring, until fragrant, 30 seconds.
Stir in vinegar, soy sauce, red-pepper flakes, and sugar.
Return chicken to pan, skin side up. Bring to a boil, cover, and reduce heat to low; cook 15 minutes (liquid should be gently simmering; adjust heat if necessary).
Uncover, raise heat to medium, and cook until sauce is reduced by half, at least 10 minutes.