Remove any skin and pin bones from salmon, then chop into 1/4-inch pieces. Transfer 1/4 of the salmon pieces to a food processor. Place remaining salmon in a large bowl.
Add mustard, mayonnaise, and lemon juice to the food processor. Pulse until a thick paste forms. Transfer mixture to the bowl with the remaining salmon. Mix in bread crumbs, scallions, and chili flakes until evenly combined.
Form salmon mixture into 4 patties. Place on a baking sheet and season with salt and pepper. Place in the freezer for 1 hour.
Preheat an air fryer to 400 degrees F (200 degrees C). Spray the air fryer basket with nonstick spray.
Place burgers in the prepared basket and spray tops with nonstick spray. Cook for 8 minutes. Spray tops again and cook for 5 minutes more.