Personally, I've never fed my bettas tropical flakes because....well, its not made for bettas, and for the most part doesn't meet the proper nutritional needs for a betta based on what I've seen. They seem to have more fillers and plants and such from what I've seen, which are difficult fora meat-eating betta to digest.
On top of that, personally, I'm just not a fan of flakes over all....in addition to the previously mentioned reasons, they're so much messier then pellets and can be hard to feed the proper amount, which is very important for a betta, because they vary so much in size and are so small and thin.
On Tropical flakes that don't provide the proper nutrition for your betta, ones with lots of plant material and fillers and such in them, IS going to effect its lifespan and general quality of life over all. However, if they are a high quality flake and you make sure they fit a bettas nutritional needs as well as offer them a variety(which is a good idea with any food you feed)of other good-quality foods and such, your betta should live just as long as any other.
Here is a great thread that, mostly focuses on pellets, does a wonderful job at describing what you should look for when picking out a commercial food for your betta.