When people call a horse flashy they usually mean that there's something eye catching about them, like a lot of white markings or bold paint patterns. Some people will call a horse with big movement (like a gaited horse) flashy in the way they move.
When people call a horse fancy they usually mean that it has the correct movement that's desired for a particular discipline. For example, if someone said their hunter was a fancy mover the horse would move in a long low floaty stride with very little knee/hock movement. But a fancy hunter wouldn't necessarily be considered a fancy dressage prospect or western pleasure horse.