Bring a large pot of salted water to a boil and cook spaghetti until al dente, then drain and set aside.
Toss the shredded rotisserie chicken with Cajun seasoning and smoked paprika.
Melt 2 tablespoons butter over medium heat.
Add the seasoned chicken and cook for 3 to 4 minutes until glossy and butter-coated, then transfer to a plate.
Melt the remaining butter and sauté garlic for 1 minute until fragrant.
Pour in the Rotel tomatoes with their juices and cook for 3 minutes.
Add chicken broth and heavy cream, stirring gently.
Add Velveeta and cream cheese, whisking until fully melted and silky.
Stir in cheddar, mozzarella, salt, black pepper, and red pepper flakes until thick and creamy.
Return the chicken and mix into the sauce.
Add the cooked spaghetti and toss until every strand is heavily coated and glossy.
Simmer for 2 minutes so the sauce clings to the pasta.
Sprinkle with fresh parsley and serve warm.