Heat the olive oil in a large skillet over medium-high heat.
Add the finely diced onion and sauté until softened, about 4–5 minutes; add the minced garlic for the last minute and cook until fragrant.
Stir in the chicken broth, uncooked orzo, undrained diced tomatoes, Italian seasoning, kosher salt, and crushed red pepper flakes; bring the mixture to a boil.
Reduce heat to a simmer, cover, and cook for 12–15 minutes or until the orzo is tender and liquid is mostly absorbed.
Uncover, add the shredded rotisserie chicken and chopped spinach, stir to combine, and cook 2–3 minutes more until the spinach wilts and chicken is heated through.
Sprinkle with the grated Parmesan, stir gently, adjust seasoning to taste, and serve.