Melt butter in a medium skillet over medium heat. Add garlic and red pepper flakes and saute 1-2 minutes until fragrant. Add wine and bring to a simmer over medium heat. Reduce heat to medium-low and allow to simmer 5-10 minutes until slightly reduced and thickened, stirring occasionally. Remove from heat and cover pan to keep warm.
Cut each chicken breast in half width-wise so you have 4 thin chicken cutlets. Pound chicken cutlets flat between two sheets of wax paper using a meat mallet or a rolling pin.
In a shallow bowl, whisk eggs and milk together until smooth. Place flour in a shallow bowl and season with salt and pepper. Place breadcrumbs in a third shallow bowl.
Dredge chicken cutlets in flour, shaking off excess. Dip cutlets in egg, then roll in breadcrumbs until fully coated. Place on a plate.
Preheat air fryer to 400F for 3 minutes. Spray basket well with pan spray, then lay chicken cutlets in a single layer (work in batches as necessary) and spray well with pan spray.
Air fry chicken at 400F 8-10 minutes until cutlets are crispy and register 165F. Repeat cooking with remaining chicken.
Arrange chicken cutlets on top of individual servings of angel hair pasta. Squeeze lemon juice over chicken and top with a few spoonfuls of white wine sauce. Garnish with parsley and serve chicken immediately. Enjoy!