Heat the large skillet over medium-high heat and add the olive oil.
Add the diced onion and sauté until soft, 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, then reduce heat to a simmer, cover, and cook 12–15 minutes until the orzo is tender and most of the liquid is absorbed.
About 3 minutes before the orzo is done, stir in the shredded rotisserie chicken and chopped spinach so the spinach wilts and the chicken heats through.
Remove from heat, sprinkle with grated Parmesan, stir to combine, and adjust salt or seasoning to taste before serving.