As far as urban slang, the definition is "to show off." Used by many rappers, most notable Ice Cube and the Geto Boys. Originated in the urban community, and has been used for quite some time.
"...no flexin', didn't even look in the nearest direction as I ran the intersection. (This is said because Ice is trying to get away from some people who tried to kill him the other day In the song, of course)" -Ice Cube, "It Was a Good Day"
by The Boston Rag February 27, 2005