Flaunt means to exhibit or parade (something) in an ostentatious manner. The definition of flout is to show contempt for or to scorn. These verbs are often confused due to their similarity in sound, but they share no meanings.
Examples
The most common error with these two words is the misuse of flaunt in place of flout—for example:
. . . the cyclists will sometimes flaunt the law and say their name is “Donald Duck” rather than giving their true identity. [Boston Globe]
The deputy head of the new government . . . threatened a special operation to depose him should he continue to flaunt the authority of the new regime. [DW World]
These writers use flaunt well:
I’d much rather proudly display my library card than flaunt an iPad. [NY Times]
In the government school where Pooja studies with her younger sister, kids don’t flaunt cell phones or make fun of the kid whose family has a mere Maruti 800. [An Indian Muslim]
And in these examples, flout is used correctly:
Fines would increase for commercial and residential buildings whose tenants flout recycling laws. [NY Post]
Anyone caught repeatedly flouting hygiene rules should be sacked. [Press and Journal]