Many people will notice an increase in their chest with incline bench presses simply because in order for the flat bench press to put the muscle under a stretched load (very important, yet overlooked for hypertrophy) with the flat bench, you must use a rather wider grip and sink deep. Dumbbells allow this more than barbells, but by doing this you put the rotator cuffs at serious risk for injury. Thusly, the flat bench press would be the best chest exercise, on par with dips, if one were able to sink deep enough without hurting the shoulders.
In order to avoid rotator cuff injury for those prone (some get by without problems), while still developing the chest, dips and incline bench presses will work wonderfully. That doesn't mean your chest won't grow with flat bench presses. It just means that the results may be sub-par.