According to the U.S. Food and Drug Administration, the term "flavor" on a product label signifies "any natural or synthetic substance or substances used solely to impart a taste to a cosmetic product." In Europe, the labeling name for flavor is "aroma". The term "flavor" is used most often for lip-care products and lip cosmetics (think lipstick, lip gloss).
Although it is basically synonomous with fragrance, listing "flavor" on products meant for application to lips is more appealing (who wants to think of ingesting fragrance?). Given that flavor can be composed of numerous ingredients, it's a gamble as to whether or not lips will experience sensitivity. Most lip plumpers listing flavor tend to use that term to encompass flavoring agents that can have a sensitizing effect of lips, such as various types of pepper, ginger, or various forms of mint.