Mix garlic, 1 tsp. salt, oregano, 1 T. vinegar, and black pepper in a large bowl, and mix well. Add the chicken pieces, and mix to cover the chicken with the spices. Set aside for about 15 minutes.
Heat 1 T. oil in a Dutch oven over medium high heat until shimmering. Add onion, green pepper, and pepper flakes. Cook while stirring until vegetables begin to soften, about 6 minutes. Add half the parsley and stir. Push the vegetables aside, and add the chicken to the cleared area. Cook 3 minutes on a side until the outer layer of the chicken is opaque, but not very brown.
Add the tomato sauce, about 2 1/2 cups of broth, and stir everything together. Bring back to a simmer, reduce the heat to low, and simmer for 20 minutes, covered.
Add rice, olives, capers, and stir well. Bring to simmer again, and place the pot in the preheated oven. After 10 minutes, remove the pot from the oven, stir to be sure that nothing is sticking to the bottom of the pot, cover again, and return to the oven for another 10 minutes. Again remove the pot from the oven, stir, and add another 1/2 cup of broth. Cover, return the pot to the ove, and cook until the chicken is done (175°F.) on an instant-read thermometer. The total time in the oven should be about 30 minutes.
Add another tablespoon of olive oil, a tablespoon of white vinegar, the remaining parsley, the jarred peppers, and another 1/4 cup of broth, and mix well. Return to the oven for 5 minutes to bring to serving temperature. If you are holding the dish for later add an additional 1/4 to 3/4 cup of broth (until the mixture is moist but not soupy), and refrigerate. Reheat slowly in the oven at 275°F. for an hour or until desired serving temperature.