Flaunt is a synonym of brandish.
In lang=en terms the difference between flaunt and brandish
is that
flaunt is to parade, display with ostentation while
brandish is to bear something with ostentatious show.
As verbs the difference between flaunt and brandish
is that
flaunt is (obsolete) to wave or flutter smartly in the wind while
brandish is to move or swing a weapon back and forth, particularly if demonstrating skill.
As a noun brandish is
the act of flourishing or waving.