Preheat oven to 250 deg. In large shallow dish, combine flour, salt, and pepper. Lightly dredge the chicken in the flour (you won't use it all, that's okay!) and set aside briefly.
Put cast iron skillet (or your favorite large pan) on medium high heat. Melt 1 tablespoon of the butter, and sear four pieces of the chicken, 2 minutes per side. Once batch A is cooked, place in the oven on a sheet pan and repeat, starting with another tablespoon of butter.
Once all 8 pieces of chicken are cooked and in the oven, add in minced garlic and stir for 30 seconds. Add in the wine, followed by the stock. Let cook for a minute, then add in the juice from both lemons and the remaining butter. Let simmer for 5 minutes.
Once the sauce has simmered, turn off heat. Add in parsley, capers, and a pinch of salt. Serve chicken immediately; I prefer sauce first on the plate!