Bring large pot of salted water to boil. Cook pasta according to box directions. Drain and set aside.
While pasta is cooking, spray a large, deep sided skillet with nonstick cooking spray. Sauté onions and peppers over medium heat until onions are mostly tender, about 5 minutes. Stir in tomatoes, chicken, and fajita seasoning.
In a small bowl, whisk flour together with chicken broth until incorporated and there are no lumps. Pour into the pan and bring to boil to thicken sauce slightly.
Add pasta and cheese to the pan and stir to coat well. Sprinkle with salt and pepper if needed, divide into four even portions and serve.