Bring a large pot of salted water to a boil. Add the orzo pasta and cook according to package instructions until al dente, about 8-10 minutes. Drain and set aside.
While the orzo is cooking, heat olive oil in a large skillet over medium heat. Season the salmon fillets with salt and black pepper. Place the salmon in the skillet and cook for about 4-5 minutes on each side, or until the salmon is cooked through and flakes easily with a fork. Remove from the skillet and set aside.
In the same skillet, add the lemon zest, lemon juice, and chopped spinach. Cook for 2-3 minutes until the spinach is wilted.
Add the cooked orzo to the skillet and toss to combine. Stir in the chopped parsley, Parmesan cheese, and red pepper flakes if using.
Flake the cooked salmon into large pieces and gently fold it into the orzo mixture.
Serve warm, garnished with additional parsley and lemon wedges if desired.