In shallow dish, combine 4 tablespoons flour and black pepper. Dredge chicken breast halves in mixture.
In large skillet over high heat, melt ¼ cup butter (1/2 stick). Add green onions; sauté over medium heat until softened, about 2 minutes. Add chicken to pan; cook, turning once, until lightly golden brown on both sides, about 3 to 4 minutes per side. Remove chicken from pan and keep warm.
Add chicken stock and wine to pan, stirring to scrape bits off bottom. Bring mixture to a boil and cook until reduced by half, about 6 minutes.
In small bowl, knead together remaining 2 tablespoons of flour and 1/4 cup butter. Whisk into sauce and stir until thickened. Stir in lemon juice and artichoke hearts. Stir in salt.
Add chicken and cook, covered, until heated through, about 7 minutes. Just before serving, add capers and chopped parsley to chicken.