There is no difference. It is just the conjugation of the verb "flaunt, flaunting.." 'flaunt' is a noun as well.

'Flaunting' is the present participle of the verb 'to flaunt' so they both mean to shamelessly parade or show off something (such as money) or to be showy and ostentatious. Did you see her flaunting her new boyfriend at the party last night? (flaunting = present participle) I have great respect for him because he never flaunts his wealth.' (flaunts = verb)

v. flaunt·ed, flaunt·ing, flaunts v.tr. 1. To exhibit ostentatiously or shamelessly: flaunts his knowledge. 2. Usage Problem To show contempt for; scorn. v.intr. 1. To parade oneself ostentatiously; show oneself off. 2. To wave grandly: pennants flaunting in the wind.