Flaunt is to show off, but flout is to ignore the rules. Rebels do both — they flaunt their new pink motorcycles by popping a wheelie, and flout the law by running a red light.

Flaunt means to work it, to preen like a peacock. You could flaunt your new Harley, your wealth, or even your bright colors:

Prosperous Chinese are less shy about flaunting their wealth than people in other countries. (Economist)

Daffodils flaunted golden cups at their more gorgeous neighbors, the tulips. (Lucy Foster Madison)

Flout, on the other hand, means to show a blatant disregard or contempt for. If you scoff when told what to do, you flout the rules. Here are some rules being flouted in the news:

In other words, the euro zone is based on a gentleman's agreement that's widely flouted. (Salon)

Baseball's rulebook is routinely ignored, flouted and evaded. (New York Times)

The problem is that people use flout to mean flaunt. If you mix up the words in the sentences above, the meaning changes. It would be weird to flout your wealth or your golden color. Garner's Modern American Usage identifies this error at widespread: it can be seen in the writing of well-educated people. However, Garner advises (and we concur) that the distinction between flaunt and flout be preserved.