As always with horses, 'it depends'.
Most lower level riders use 'flashy' to indicate a horse has a bright, pretty color (especially chestnut or a light bay) and lots of white markings. White markings are all the vogue these days, even in the hunter show ring. 'Flashy' is how the white markings look to the novice, as the horse moves (however it actually moves).'Flashy' is often used for a nicely marked Pinto or Appaloosa, or a Palomino with a nice deep vibrant gold color.
A lot of more experienced riders use 'flashy' to mean something entirely different. In this next meaning, it has nothing to do with color or markings.
Sometimes in this next sense, it's interchangeable with 'fancy'.
If they're hunter riders, they may use the term for a well balanced horse that sweeps over the ground with the desirable straight knee and hock and yet a little 'push' off the ground that takes the horse forward with a little bit of suspension (time in canter or trot when all 4 feet are off the ground). It's not a big upward bounce, but more like a float forward over the ground with all 4 feet not bearing weight. That goes back to the original use of hunters, to efficiently cover the ground (though the most efficient use of energy is NO suspension, SOME suspension is liked in the show ring).
If they're dressage riders, 'flashy' or 'fancy' might be the word for a horse that really lifts its knees and bends its hocks, and yet still floats forward over the ground, but the 'suspension' (all 4 feet clear of ground and not bearing weight) is different than the hunter, instead of JUST a float forward over/across the ground, it's both floating across the ground AND bouncing way up in the air.
Here's the ultimate dressage bouncer - Quatarback - no artificial devices to teach this - no long feet or heavy shoes - this is 'just him' - with a little encouragement from the crowd -
Quaterback having fun at home:
He isn't just a good bouncer though, he's also extremely fluid and well balanced. Just sit up, hang on and smile.