A word like ‘flamboyant’ can be applied to so many things, which is why it is not possible for the dictionary to be specific about the sort of ‘display’. It depends on the context.
The Las Vegas showgirls put on a flamboyant show.
in this case their costumes, dancing and make up, combined with the lighting and make up is the ‘display’, and their dancing, poses, moves and scenery is the colourful behaviour.
The peacock attracts his mate with an elaborate ritua.
in this case the peacocks tail feathers make the ‘display’ and the way in which he moves to display them is the colourful behaviour.
“Flamboyant” is also a code word for showy effeminacy in men known or presumed to be homosexual. At least that’s true in the United States anyway. The media really likes to use it this way. It often has a derisive or disdainful air.