Place the chicken in a 5 or 6-quart crock pot. Combine the wine, tomato paste, garlic, basil, oregano and salt in a small bowl; pour over chicken. Add the chicken broth, reserving 1/4 cup of it. Cover and cook until the chicken is tender, 4-5 hours on high or 8-10 hours on low. Cover and refrigerate the remaining chicken broth.
About 40 minutes before the cooking time is up, wisk the reserved chicken broth , the vinegar, and flour in a small cup until smooth. Gradually stir the flour mixture into the liquid in the crock pot without disturbing the chicken. Add the beans and sliced tomatoes in layers. Cover and cook on high until the mixture simmers and the beans are tender, about 35 minutes.