Bring a large pot of lightly salted water to a boil. Cook spaghetti in the boiling water, stirring occasionally, until cooked through but firm to the bite, about 12 minutes. Drain.
Melt butter in a large skillet over medium-high heat; saute onion, celery, and bell pepper in hot butter until softened and translucent, 5 to 10 minutes. Whisk mushroom soup, Cheddar cheese, and flour into onion mixture until cheese melts and mixture is smooth. Add broth and stir until smooth.
Stir chicken, cooked spaghetti, almonds, mushrooms, pimento peppers, salt, and celery salt into cheese mixture. Pour into an 11x13-inch baking dish and sprinkle crushed buttery round crackers over the top.
Bake in the preheated oven until golden and bubbling, 15 to 20 minutes.