Cosmetic Fragrance and Flavor Ingredient Right to Know Act of 2023 This bill imposes disclosure and labeling requirements on cosmetic products that contain certain ingredients. A cosmetic product that fails to meet such requirements may not be sold. Within two years of this bill's enactment, a cosmetic product's labeling or packaging must include a full list of its ingredients, as well as a specified statement that directs consumers to the brand owner's website for the health impacts of any ingredient that (1) is identified on specified lists of harmful or potentially harmful chemicals, such as chemicals identified as carcinogenic to humans by the Environmental Protection Agency or toxic air contaminants under California regulations; or (2) must be disclosed under certain European Union laws and is present in a product above specified concentrations. The Food and Drug Administration must publish and periodically update on its website a list of the ingredients subject to this requirement. Within one year of this bill's enactment, a brand owner must disclose the full list of ingredients for each cosmetic product on its website, as well as whether a cosmetic product contains any fragrance or flavor ingredient that is subject to this bill's labeling or packaging requirement and, if so, the ingredient's functional purpose.