Place flour in a shallow bowl; season with salt and pepper. Dredge chicken in flour, shaking off excess.
In a medium skillet, heat 1 tablespoon oil over medium-low. Add chicken, skin side down. Cook until skin is browned, 8 to 10 minutes. Turn over, and continue to cook, 8 to 10 minutes more.
Meanwhile, in a small bowl, whisk together vinegar and remaining tablespoon oil. Add parsley, and season with salt and pepper; drizzle dressing over tomato. Serve with chicken.
For a crisp skin and succulent interior, cook chicken thighs over low, steady heat, and don't turn them over too soon.