Cook the pasta according to package instructions in a large pot of salted boiling water until al dente. Reserve 1/2 cup of pasta water, then drain the pasta and set aside.
In a large skillet, heat the olive oil over medium heat. Add the minced garlic and red pepper flakes (if using) and sauté for about 1 minute until fragrant.
Add the cherry tomatoes to the skillet and cook for 3-4 minutes until they start to soften.
Stir in the fresh spinach, salt, and black pepper, cooking until the spinach wilts, about 2 minutes.
Add the drained canned salmon and the cooked pasta to the skillet. Toss everything together, adding reserved pasta water a little at a time until the desired consistency is reached.
Drizzle with lemon juice and sprinkle with Parmesan cheese. Toss again to combine.
Serve immediately, garnished with fresh parsley.