Training under Luke Skywalker
In order to get a better picture on how much knowledge Kylo Ren, as Ben Solo, had access to, there will be looked at the knowledge Luke Skywalker, Ben’s Jedi Master, gathered during his lifetime up to the point of the destruction of his Order at the hands of Kylo Ren.
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First of all, Luke by Return of the Jedi was trained by Yoda, the Grandmaster of the Prequel Trilogy Jedi Order, to not only be a full-fledged Jedi but also be capable of starting a new Jedi Order and pass down his knowledge.
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“No more training do you require,” Yoda assured him. “Already know you that which you need.”
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--Return of the Jedi novelization
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“Luke—of the Emperor beware. Do not underestimate his powers, or suffer your father’s fate you will. When gone I am … last of the Jedi will you be. Luke, the Force is strong in your family. Pass on what you … have … learned …”
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--Return of the Jedi novelization
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Secondly it’s mentioned in Bloodline and in Star Wars Character Encyclopedia: Updated and Expanded that Luke studied the Force and gathered long lost Jedi knowledge when the Galactic Empire was defeated.
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“They say on my world that the Force sometimes runs strong in certain families.” So much of the lore of the Jedi had been lost—but on Gatalenta, the old religion had remained strong. History had become legend, but some of the legends were still told. Gatalenta had been one of Luke’s first destinations when he began his research into the Jedi Knights of old.
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--Star Wars Bloodline
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“After the Empire is defeated, Luke undertakes much study, travel, and spiritual contemplation, before committing to pass his knowledge on to a new generation of Jedi Students.”
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--Star Wars Character Encyclopedia: Updated and Expanded
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Furthermore the Star Wars Character Encyclopedia also mentions that Luke gained knowledge from the famous explorer Lor San Tekka, who’s said to have uncovered much of the Jedi History (The Force Awakens Visual Guide), possess many Jedi secrets (The Force Awakens Visual Guide) and discovered many fragments of ancient Jedi traditions (Star Wars Character Encyclopedia: Updated and Expan
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In his travels, Lor San Tekka uncovered much of the history of the Jedi Knights that the Galactic Empire had tried so hard to erase.
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--The Force Awakens Visual Guide
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Others now seek him for his knowledge of Jedi Secrets.
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--The Force Awakens Visual Guide
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Lor San Tekka uncovered many fragments of the ancient Jedi traditions that the Old Empire had worked so hard to destroy. When Luke Skywalker began researching Jedi history in the hope of restoring the Jedi Order, he learned much from Lor San Tekka.
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--Star Wars Character Encyclopedia Updated and Expanded
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Additionally it’s mused by Leia Organa that there isn’t a Jedi ruin that Lor San Tekka hasn’t explored.
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-- Poe Dameron 001
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Dark Side Knowledge
The Force Awakens Visual Guide acknowledges that Kylo Ren studied arcane (= very rare) Dark Side lore.
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Having studied Jedi skills as well as arcane dark side lore, Kylo Ren is the embodiment of conflict, drawing upon contradictory teachings and deriving power from discord.
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--The Force Awakens Visual Guide
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Knowledge about Lightsaber Combat
He created his crossguard lightsaber based on an ancient design dating back to the Scourge of Malachor, this implies that he had access to ancient knowledge.
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Kylo Ren’s unusual lightsaber is an ancient design, dating back thousands of years to the Great Scourge of Malachor.
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--The Force Awakens Visual Guide
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Jedi Knowledge
Kylo Ren could have access to Jedi Knowledge and possibly at least part of the Jedi Archives because we know that the First Order pulled out the map to the First Jedi Temple out of the old Imperial Archives while at the same time we know that the Grand Inquisitor studied these Jedi Archives.
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"I am familiar with general droid technical specifications. I don't need to acquire one: What I want is located in it's memory. It's carrying a section of a transgalactic navigational chart. We have the rest, recovered from the archives of the Empire."
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--The Force Awakens novelization
Training under Supreme Leader Snoke
Likewise we can take a look at the knowledge Kylo Ren’s master Supreme Leader Snoke possessed.
Supreme Leader Snoke, who trained Kylo Ren, is said to be steeped in Dark Side knowledge.
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Kylo Ren is the most gifted apprentice of Supreme Leader Snoke, a mysterious figure steeped in dark side knowledge who commands the First Order from a distance.
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--The Force Awakens Visual Guide
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To put Snoke's knowledge better in perspective we can take a look at the canon novel Dark Disciple where Darth Sidious's involvement with the Dark Side is described as 'steeped'.
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"Darth Tyranus," intoned Count Dooku's Master. Even though he wasn't physically present, the simple sound of his voice - rasping, papery, somehow, like the rustling of ancient parchment - sent a shiver through Ventress. This man was steeped in the dark side of the Force, saturated with it, in a way that she was certain Vos, perhaps even Dooku, had never been.
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--Star Wars Dark Disciple
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