Heat the bacon grease in a skillet, until it's partially melted. Add the flour, stirring well to combine. Allow it to cook for 2 to 3 minutes, or until the mixture begins to thicken.
Add the milk, stirring constantly to get rid of any lumps. Cook for 5 minutes, stirring often, until the gravy thickens.
Add the salt, pepper, and cayenne, stirring well. Add more salt to taste, then serve immediately.