Cut the chicken breasts in half and slice them lengthwise. Season the cutlets with salt and pepper.
In a skillet, heat 4 Tbs olive oil over medium-high heat. Sear the cutlets, working in batches if necessary to not to overcrowd the pan, about 2 minutes per side and cooked through. Transfer the chicken pieces to a platter.
Add 4 Tbs olive oil to the skillet and cook garlic, stirring, until soft but not brown, about 2 minutes. Add the capers and port, scraping the bottom of the pan, and cook on medium heat for about 3 minutes. Add the butter and lemon juice and swirl the skillet until the butter melts and forms a sauce with the rest of the ingredients. Sprinkle with the flour and stir until sauce thickens slightly, about 1 minute.
Pour the sauce over the chicken in the platter. Sprinkle with some minced parsley if desired.
Notes
You can serve it with simply boiled baby potatoes, perfect to soak up the sauce