Cut the chicken crosswise into ½-inch thick slices. Sprinkle with salt and pepper. Spread some (about 2 tablespoons) flour on a plate. Dredge chicken in flour to coat.
Heat 1½ tablespoons oil in a large skillet over medium heat. Add the chicken and cook until just cooked through (feels springy to touch and opaque in the center), about 1½ minutes on each side. Transfer the chicken to a clean plate.
Add 1½ tablespoons oil to the skillet and increase the heat to medium-high. Add the vegetables. Sprinkle with salt and pepper and sauté until no longer look raw on the outside, stirring frequently, about 2 minutes. Add the broth and bring to a boil, stirring up the browned bits on the bottom of the pan. Cover the pan and boil until the vegetables are almost tender, about 3 minutes for zucchini.
Return the chicken to the pan. Add the green onions and lemon and simmer until the sauce thickens and coats the chicken, stirring constantly, about 2 minutes. Add any optional flavorings. Taste and adjust the salt and pepper. Serve right away.