1. Bring a large pot of salted water to a boil. Place flour in a shallow bowl. Season cutlets with salt and pepper, then dip into flour, turning to coat; shake off excess.

2. In a large skillet, heat 1 tablespoon oil over medium-high. Add half the chicken; cook until lightly browned and opaque throughout, 1 to 2 minutes per side. Transfer to a plate; cover with foil to keep warm. Repeat with remaining tablespoon oil and chicken (reserve skillet for sauce).

3. Meanwhile, cook linguine in boiling water until al dente, according to package instructions. Reserve 1/2 cup pasta water. Add spinach, and stir until submerged. Drain pasta mixture and return to pot. Toss with 1 tablespoon butter; season generously with salt and pepper. Add some reserved pasta water if necessary. Cover to keep warm.

4. Into skillet, pour wine and lemon juice. Cook over medium-high, stirring to loosen browned bits, until liquid has reduced to 1/3 cup, 4 to 5 minutes. Remove from heat; swirl in 2 remaining tablespoons butter until melted. (For a smoother sauce, strain through a fine-mesh sieve, if desired.) Add capers, and season with salt and pepper. Divide chicken and linguine among four serving plates; top chicken with sauce.