When a person boasts, they're actively speaking of or describing something. "He liked to boast about his high-paying career, a habit which his friends barely tolerated." The term "boast" can also be used when describing the features of a thing, usually when talking it up or attempting to sell it. "The sprawling mansion boasts seven bathrooms and nearly a dozen bedrooms." "Flaunt", however, is not conversational. Flaunting something is very action-based - you can't flaunt ABOUT something; you simply flaunt it. In other words, you don't have to boast about the thing - your actions do it for you. Flaunting is, essentially, non-verbal boasting. It might still be obvious that you're doing it, but it isn't quite as overt as simply pointing it out in a blunt statement. "She was known to flaunt her wealth by carrying expensive bags and wearing only the most exclusive designs." "He flaunted his powerful physique by flexing his muscles whenever he felt that someone was watching him." Boasting, except when used as a way to highlight a selling point or feature, is done vocally. Flaunting is done through action, and doesn't necessarily involve talking about it.

Flaunt means that you don't talk about it all you do is show it. While boast means that you talk about it all the time. He BOASTS about his great wealth ( he talks about it all the time) He FLAUNTS his great wealth (he buys big houses, expensive cars, but he doesn't necessarily talk about them)

flaunt means to show aggrogance boast means talk with excessive pride and self-satisfaction about one's achievements, possessions, or abilities. "she boasted about her many conquests"