In the same large pot, heat the olive oil over medium heat. Add the onion, garlic, salt, paprika, black pepper, and red pepper flakes. Cook, stirring frequently, until lightly golden, 3 to 4 minutes. Add the chicken broth, vinegar, sugar, and the strained smoked turkey stock. Add the greens one handful at a time, stirring until wilted. Fold in the shredded turkey. Add water until it just covers the greens. Cover and cook until the greens are tender, 45 minutes to 1 hour. Remove the lid and simmer until the liquid is slightly reduced, 10 minutes. Taste for salt and vinegar.