Samsung will be first out of the gate with a flexible display device. Unfortunately, people in the know are saying that the technology just isn't ready yet, and so there is little chance that it would make it into the Galaxy S IV, especially with the expected launch just a few months away.There has been a lot of chatter recently about flexible displays, or as they are bound to be marketed, "unbreakable" displays, and there has been a report saying that
Of course, starting with the HTC DROID DNA, it looks like 1080p is the new standard for flagship devices, so that's almost a certainty for the Galaxy S IV. But, it looks like it may be more reasonable to expect the Galaxy Note III to have a flexible display, since that device likely won't be out until later in the year.
source: The Verge