Cook pasta in salted boiling water according to package directions. Reserve 1 cup pasta water when draining.
In a skillet, heat 1 Tbsp. olive oil over medium heat. Add 1 clove minced garlic and cook for about 30 seconds. Add zucchini and cook until tender, stirring often. Remove to a bowl.
In the same skillet, heat 1 Tbsp. olive oil over medium-high heat. Cook chicken until done. Remove to a plate.
While the chicken cooks, whisk together flour and milk in a bowl.
After chicken is done, add remaining 1 clove garlic and 1 Tbsp. oil in the skillet. Cook on medium-high heat for 30 seconds.
Add flour mixture and bring to a boil, stirring constantly. Reduce heat to low and stir for 2 minutes.
Add evaporated milk, 1/2 tsp. salt, and parmesan cheese. Stir until cheese melts.
Cut chicken into strips. Add to pasta along with zucchini and sauce. Add reserved pasta water to loosen, if needed.