Add 3 tablespoons of the flour to a shallow dish or plate then slice the chicken breasts horizontally making thin cutlets.
Season the cutlets on both sides with salt and pepper then dredge the cutlets in flour.
Heat the olive oil and 1 tablespoon of butter in a large skillet over medium to medium-high heat. Add the chicken without overcrowding searing both sides to golden (about 3-4 minutes per side) then remove to a plate. The chicken may not be cooked through at this point.
Reduce the heat to low then add 2 tablespoons of butter and 2 tablespoons of flour to the skillet. Stir to combine and cook 1 minute then add the wine to deglaze, scraping up any brown bits from the bottom of the skillet.
When the wine starts to reduce, pour in the chicken stock and juice from 1/4 of the lemon and cook over medium heat letting the sauce thicken. Taste and adjust salt and pepper if needed and if you prefer a more lemony flavor, add the juice from another 1/4 of lemon.
Return the chicken to the skillet then fold in the drained capers and artichokes and cook 5-7 minutes (or until the chicken is cooked through), spooning some of the sauce over the chicken. Garnish with parsley and (optional lemon slices) then serve right away.