To flaunt means "to show off." To flout means "to defy" or "to show contempt for."

Examples:

• She didn't flaunt her wealth while bread lines snaked down city blocks.
• Poorer countries have a harder time demanding sacrifices from their people when rich countries flout the rules.
• Drivers are still flouting the law and using their cell phones on the road despite facing hefty penalties.

Corrections:

• "David McClintick's Indecent Exposure is one of the best books about moral turpitude in modern Hollywood. But the otherwise-savvy author uses flaunt for flout, thereby injuring two words at once: 'To Cliff Robertson, Columbia's reinstatement of Begelman was not only a brazen flaunting of justice, but also a deep insult to Cliff personally.' In a single sentence, an author who has convinced you that he could write anything leads you to suspect that he has read nothing."
  (Clive James, "Georg Christoph Lichtenberg: Lessons on How to Write." Cultural Amnesia, 2007)

• "'Oscar Wilde was jailed, exiled and ruined,' wrote John Lahr in The New Yorker, in a piece about Woody Allen, 'for flaunting sexual convention offstage as brazenly as his epigrams undermined social convention on it.'
  
  "That's a finely honed sentence, contrasting differing conventions by stressing the adjectives social and sexual and playing the syllable off against the concluding stressed word on. Even the de-emphasized last pronoun it was well chosen, because its alternative--onstage--would have made the sentence too determinedly balanced.
  
  "Only one problem: flaunting was a mistake.
  
  "To flaunt means 'to display proudly, even ostentatiously,' the way a peacock shows its feathers; indeed, an early use of the word in 1576 was set in the phrase 'whose fethers flaunt, and flicker in the winde.'
  
  The word that fit the context of The New Yorker's piece on Allen was flout, which means 'to jeer, deride, scoff at, show contemptuous disregard for,' first cited in a 1551 translation of Sir Thomas More's Utopia: 'in moste spitefull maner mockynge . . . and flowtinge them.'"
  (William Safire, "If You Got It, Flaunt It." The New York Times, April 27, 1997)

Practice:

(a) Though picture-taking is forbidden inside the cathedral, many visitors openly _____ the ban.

(b) He finds himself surrounded at school by sneering aristocrats who _____ their pedigrees and wealth as badges of their superiority.
Answers to Practice Exercises

Glossary of Usage: Index of Commonly Confused Words