It's no secret that Star Wars: The Force Awakens shared a lot of similarities with the original trilogy, specifically Star Wars: A New Hope. Adam Driver's Kyle Ren is meant to be the new Darth Vader for this trilogy, and it helps that the character actually does have an obsession with the deceased Sith Lord. It sounds like his obsession will carry over into Star Wars 8 and may even be reflected in his costume.
A new report from the very reliable fan site Making Star Wars claims Kylo Ren will be furthering his obsession with Darth Vader in Star Wars: Episode VIII. This obsession will reportedly manifest visually and be reflected in the form of Kylo Ren trading in his cloak from Star Wars: The Force Awakens for a Darth Vader cape. Here is how Making Star Wars explains it.
"According to sources, Kylo Ren is wearing a Darth Vader cape in Star Wars: Episode VIII. The cape is said to be like the one Darth Vader wears in The Empire Strikes Back/Return of the Jedi. However, the cape does not have the same chain clasp. It is not entirely clear if this cape is one Kylo made to resemble that of his grandfather's or if he actually procured one of Darth Vader's capes that probably fell into the hands of collectors in the Star Wars galaxy."
Since Kylo Ren *spoilers* killed Han Solo at the end of Star Wars: The Force Awakens, it seems like his internal struggle is going to be less of an issue and that he is going full on Dark Side this time around. At the very least, he is pretty much irredeemable at this point. So it would definitely make sense that he would want to more closely resemble Darth Vader in Star Wars: Episode VIII and trade in his emo hoodie/cloak for his grandfather's cape. It also isn't out of the realm of possibility that he could wind up wearing an actual Darth Vader cape. After all, he did manage to obtain Darth Vader's helmet somehow.
One thing that was made clear in Star Wars: The Force Awakens is that relics from the Imperial era have become collectible and probably worth good money in a galaxy far far away. So it definitely seems possible that Kylo Ren would be able to procure Anakin Skywalker's cape. The report does make it clear that the origins of the cape aren't known. It could very well wind up being one that Kylo Ren has made himself. It is also possible that this report winds up not being true as it isn't coming from an official source but as mentioned, Making Star Wars does have a pretty solid track record, generally speaking.
Very little is known about Rian Johnson's follow up to Star Wars: The Force Awakens at the present time. We haven't even been given an official title yet. Disney is clearly focusing heavily on Rogue One: A Star Wars Story right now, which will actually feature Darth Vader (and his cape) in the flesh, or at least costume covered flesh. At the moment it seems like we will have to wait until Rogue One hits theaters to learn more official details about Star Wars: Episode VIII. It is possible Disney and Lucasfilm will attach a teaser to Rogue One when it comes out, but we will have to wait and see. Rogue One: A Star Wars Story is due in theaters on December 16, with Star Wars Episode VIII is set for release on December 15, 2017.