Preheat oven to 350°F. Pat chicken dry with paper towels, then season all over with salt. Heat oil in a large skillet over medium-high. Cook chicken, skin side down, until golden brown , 7 minutes. Flip and cook another 3 minutes. Transfer chicken skin side up to a 9x13" baking dish, leaving any fat in the pan.
Return skillet to medium heat and add onion and garlic. Cook, stirring often, until onion is golden brown, 6–8 minutes. Stir in dried tart cherries (or barberries), turmeric, red pepper flakes, cinnamon and cook, stirring, until fragrant, about 30 seconds. Pour in vinegar and 1 cup water, season lightly with salt, and bring to a simmer.
Pour sauce on and around chicken pieces, then nestle orange halves, cut side up, around chicken.
Transfer pan to oven and bake, uncovered, until sauce is reduced and chicken is cooked through (165°F internal temp), 30–35 minutes (or 20–25 minutes for separated thighs, drumsticks and wings).
Serve with sauce over chicken pieces, then squeeze juice from orange halves on top.