We aren't putting much stock in one part of this rumor today. Supposedly, Samsung has nearly perfected their 3-sided flex display technology and it is heading for test production now. This isn't the part that makes us skeptical though.
The other part of the rumor is that it could end up in the Galaxy Note 4. The reason this seems unlikely is that the Galaxy Note 4 is due to launch at the beginning of September. That gives Samsung a few scant weeks to finish the testing process and send the device into full production in order to begin selling it before (or at the same time as) the iPhone 6.
This seems to contradict rumors that the Galaxy Note 4 will launch at the beginning of September. It is certainly possible that this display could end up in a different version of the Galaxy Note 4 sometime down the line. Maybe Samsung plans to do what they did with the Galaxy S5 and offer a more premium LTE-A version for the Korean market that includes this new display tech.
We should know something more concrete in September either way.
Source: AndroidAuthority