Bring a large pot of salted water to a boil. Add the elbow macaroni and cook according to package instructions until al dente, about 8 minutes. Drain and set aside.
While the pasta cooks, heat olive oil in a large non-stick skillet over medium heat.
Add the chicken pieces to the skillet, season with 1/4 teaspoon salt and 1/8 teaspoon black pepper, and cook until the chicken is cooked through and no longer pink in the center, about 6-8 minutes. Remove from heat and set aside.
In a medium saucepan, whisk together the flour and 1/2 cup of the milk until smooth to make a slurry.
Place the saucepan over medium heat and gradually whisk in the remaining 1 1/2 cups of milk. Continue whisking until the mixture thickens and begins to bubble, about 5 minutes.
Reduce heat to low and stir in the shredded cheddar and mozzarella cheeses until melted and smooth.
Add garlic powder, onion powder, smoked paprika, and the remaining 1/4 teaspoon salt and 1/8 teaspoon black pepper to the cheese sauce. Stir to combine.
Add the cooked macaroni and chicken to the cheese sauce and gently stir until everything is evenly coated and heated through, about 2 minutes.
Remove from heat and serve immediately.