Well, it's claimed that the knowledge died with Kun, not Nadd, in JATM. So Kun probably did have access to that knowledge. As for how quickly he studied it, no idea.
The Fact File quote is this:
The most powerful and dangerous of all Sith Lords, Exar Kun was once the apprentice of Jedi Master Vodo-Siosk Baas.-- The Official Star Wars Fact File #1
The TCSWE quote is this one (retconned to be "once the most powerful", so that Palpatine could remain supreme):
Once the most powerful and dangerous of the Dark Lords of the Sith, he [Exar Kun] was responsible for the deaths of millions four millennia before the rise of the Empire.-- The Complete Star Wars Encyclopedia