Place each chicken breast between plastic wrap and flatten with a meat mallet to about 1/2 inch thickness.
Season both sides of the chicken with kosher salt and pepper, then coat lightly with the flour, shaking off excess.
Heat 2 tablespoons of the olive oil in a large skillet over medium-high heat. Add the chicken and sauté until lightly browned and cooked through, about 3–5 minutes per side depending on thickness. Transfer chicken to a plate and keep warm.
Add the remaining olive oil to the same skillet over medium heat. Add the sliced garlic and the white parts of the scallions and sauté until fragrant and softened, about 1 minute.
Pour in 1 cup of chicken broth and stir, scraping up any browned bits from the bottom of the pan.
Add the halved artichoke hearts and sliced sun-dried tomatoes to the skillet and simmer until heated through and the sauce thickens slightly, about 3–4 minutes. Taste and adjust seasoning with salt and pepper.
Meanwhile, bring 2 cups of chicken broth to a boil in a saucepan. Add the Israeli couscous and cook until tender, about 8–10 minutes. Drain any excess liquid.
Serve the seared chicken over the cooked couscous, spoon the artichoke and tomato sauce over the chicken, and sprinkle with the remaining green parts of the scallions.