Cook linguine in well-salted boiling water until al dente. Reserve ½ cup pasta water, then drain.
Season chicken with salt and pepper. Heat olive oil in a large skillet over medium-high heat.
Sear chicken until golden and cooked through. Remove, rest briefly, then slice.
Reduce heat to medium. Melt butter in the same skillet and add garlic, red pepper flakes, and paprika. Cook until fragrant (about 30 seconds).
Stir in lemon juice and parsley.
Add cooked pasta and sliced chicken to the skillet. Toss to coat, adding reserved pasta water as needed for a silky sauce.
Taste, adjust seasoning, and serve immediately with Parmesan if desired.