Roll the pomegranates on the counter while applying pressure for a couple of minutes. Hold the pomegranate over a pot and cut into it with a small sharp knife. The juice will come rushing out. Squeeze the pomegranates until 3/4 to 1 cup of juice is produced. Store-bought pomegranate juice can be used when fresh are not in season. Add the vinegar, peppercorns, cloves and the bay leaf. Bring to a boil over medium heat, then turn the heat down to a simmer and reduce the liquid by half, about 6 minutes.
Meanwhile, cover the chicken with plastic wrap on meat safe board and pound to 1/4-inch thickness. Season the chicken on both sides with salt and pepper, to taste.
Heat a large nonstick skillet over medium-high heat with 2 tablespoons extra-virgin olive oil. Heat a second medium-sized skillet over medium-high heat with 2 tablespoons extra-virgin olive oil, 2 turns of the pan. Add the pancetta to the smaller skillet and cook until crisp, about 2 to 3 minutes. Add the potatoes and shallots in thin layer and season with a little salt and black pepper, to taste, and the red pepper flakes. Cook, turning occasionally, for 8 to 10 minutes. In the larger skillet add the chicken and cook for 8 minutes, turning once. Remove the chicken to serving plates. Strain the reduced pomegranate sauce into the skillet with the chicken and scrape up any bits from the bottom of the pan, then turn off the heat.
Add the arugula to a large bowl and drizzle with the lemon and about 2 tablespoons of extra-virgin olive oil. Season with salt and pepper, to taste.
Spoon the pomegranate sauce over the chicken. Top the chicken with the salad and figs and serve the potato hash alongside.