Cook the pasta in a large pot of salted water according to the package directions until al dente. Drain it and set it aside, reserving a little pasta water.
In a small bowl, toss the diced chicken with the paprika, oregano, garlic powder, thyme, black pepper, and salt until evenly coated.
Heat olive oil in a large skillet over medium heat. Sear the chicken for 3 to 4 minutes per side, or until fully cooked and the internal temperature reaches 165 degrees F. Transfer the chicken to a plate.
In the same skillet, melt the dairy-free butter. Add the minced onion, Italian seasoning, garlic powder, and salt. Cook for about 1 minute.
Stir in the gluten-free flour and mix well, scraping up anything stuck to the bottom of the pan.
Slowly pour in the chicken broth and dairy-free heavy cream. Add the spinach and whisk until combined. Simmer for 3 to 4 minutes, stirring often, until the sauce starts to thicken.
Stir in the dairy-free parmesan and cook until it melts and the sauce becomes creamy.
Add the cooked pasta to the skillet and toss to coat. If the sauce feels too thick, add a splash of reserved pasta water.
Stir the chicken back in, mix everything together, and serve warm.