Preheat the oven to 350 degrees. Season the salmon with salt and pepper and place on a parchment lined baking sheet skin side down. Bake in the oven for 10-15 minutes, until just cooked through but still pink inside. Set aside. Once the salmon is cool enough to handle break it into large flakes.
Meanwhile, heat 3 tablespoons of olive oil in a skillet over medium heat. Add the capers and garlic and fry for a few minutes. Add the lemon zest, salt and red peppers flakes, turn off the heat and set aside.
Bring a pot of salted water to a boil. Add the fettuccine and cook, stirring occasionally until tender. Drain and rinse the pasta in cool water. Place the pasta in a bowl and add the salmon, the remaining 3 tablespoons olive oil, the lemon juice, the fried capers, garlic,lemon zest, salt and red pepper flakes, parsley, and dill. Toss to combine. Serve with grated parmesan.