Add the flour to a shallow bowl and season with salt and pepper. Heat a large skillet over medium-high, then add the oil.
Meanwhile, dredge the chicken in the flour, shaking off any excess. When the oil is shimmering, add the chicken to the pan and fry until golden brown and cooked through, 4 to 6 minutes per side. Transfer to a plate and set aside.
Carefully add the wine to the pan. Using a wooden spoon, scrape up any brown bits on the bottom of the pan to release the flavor, then add the garlic, cream, parmesan, lemon zest and juice, and a little more salt and pepper. Bring to a simmer and continue cooking until the sauce thickens slightly, 2 to 3 minutes.
Taste and adjust the seasonings with a little more salt and pepper as necessary, then stir in about three-fourths of the parsley, dill, chives, and basil. Return the chicken to the pan, turning to coat. Sprinkle with the remaining herbs and serve immediately with more lemon wedges.
