Place 1 tablespoon flour on sheet of waxed paper; coat chicken; shake off excess. With cooking spray,coat large nonstick skillet; heat over medium-high heat. Add chicken; cook, turning once, 4 minutes, until browned. Cover; reduce heat to medium-low; cook, turning occasionally, 5-7 minutes, until no longer pink at center. Remove to cutting board. Let cool 5 minutes. Slice 1/4 in. thick, halve slices lengthwise.
Meanwhile, in large pot, bring 4 quarts water and 1 teaspoon salt to a boil. Add past; cook according to package directions. Add spinach; cook 10 seconds, until wilsted. Drain; return to pot.
Wipe out skillet; with cooking spray, coast skillet; heat over medium-high heat.. Add onioon; cook, stirring occasionally, 7 minutes until weel borwwned and carmalized. Stir in 1 1/4 cups broth, the lemon zest and juice, garlic, pepper and remaining salt; simmer 2 minutes. Whisk together remaining 1/4 cup broth and remaining 1 tablespoon flour in small glass measure; stir into simmering mixture. Simmer, stirring, 2 minutes, until slightly thickened. Add thyme and butter, swirl skillet until butter melts. Stir in chicken. Remove from heat.
Pour chicken mixture over pasta and spinach in pot; toss to mix. Spoon into 4 pasta bowls.