Preheat air fryer to 400°F. Pat salmon dry, brush with oil, season with salt and pepper. Air fry skin-side down 8 minutes to 145°F internal. Set aside.
Boil salted water and cook linguine to al dente. Reserve ½ cup pasta water, then drain.
Melt butter in large skillet over medium. Cook shallot 2 minutes, add garlic 1 minute. Add cream, simmer 3 minutes.
Remove pan from heat. Stir in lemon juice, zest, red pepper flakes, and Parmesan. Thin with pasta water as needed.
Toss linguine in sauce. Peel skin from salmon, flake into chunks, fold gently into pasta. Top with parsley and serve.