Bring a large pot of salted water to a boil. Add the linguine and cook until just al dente (firm to the bite). Before draining, scoop out about 1 cup of pasta water and set it aside, then drain the pasta.
Heat olive oil in your skillet over medium-high heat. Season chicken pieces with smoked paprika, garlic salt, salt, and black pepper. Place them in the hot skillet in a single layer and cook for 3–4 minutes per side, until browned and cooked through (internal temp ~165°F). Remove chicken and set aside.
Reduce heat to low-moderate. Add half of the cowboy butter to the same skillet and let it melt. Stir in garlic salt and red pepper flakes. Pour in heavy cream and stir until combined, scraping up browned bits from the pan.
Add the linguine and chicken back into the skillet. Toss gently to coat everything in sauce. If needed, add some reserved pasta water a splash at a time to loosen the sauce until silky.
Stir in fresh lemon juice to brighten flavors. Plate the pasta and chicken, then top with chopped parsley and lemon slices. Serve promptly.