Cook pasta according to package. Reserve 2 cups starchy pasta water before draining.
Meanwhile, toss chicken pieces in flour, garlic salt, and pepper.
Heat 2 tablespoons oil in a large non-stick skillet over medium-high heat and add chicken. Cook and stir 5-6 minutes until done. Remove from pan and cover.
Heat the remaining 2 tablespoons oil in the pan over medium heat and add the mushrooms, tomatoes, and garlic. Cook and stir for 4-5 minutes until mushrooms are tender. Add the chicken back as well as the spinach and cook 1-2 minutes until the spinach is almost wilted. Remove pan from heat.
Once the pasta is cooked and drained, place it back in the pot along with the goat cheese and 1 cup reserved starchy pasta water. Toss until the cheese melts and forms a creamy sauce (add the remaining reserved water if you want the sauce to be thinner). Mix in the chicken and vegetables and serve topped with fresh basil and Parmesan cheese.