Antiquities XX, 8, 9
Now when Porcius Festus was sent as successor to Felix by Nero, the principal of the Jewish inhabitants of Cesarea went up to Rome to accuse Felix; and he had certainly been brought to punishment, unless Nero had yielded to the importunate solicitations of his brother Pallas, who was at that time had in the greatest honor by him. Two of the principal Syrians in Cesarea persuaded Burrhus, who was Nero's tutor, and secretary for his Greek epistles, by giving him a great sum of money, to disannul that equality of the Jewish privileges of citizens which they hitherto enjoyed. So Burrhus, by his solicitations, obtained leave of the emperor that an epistle should be written to that purpose. This epistle became the occasion of the following miseries that befell our nation; for when the Jews of Cesarea were informed of the contents of this epistle to the Syrians, they were more disorderly than before, till a war was kindled.
I just heard a theory that the Greek Epistles are the New Testament letters commissioned by Nero essentially asserting that Nero (or his wife) created Christianity. I'm not asking whether you are a believer or not (of which I certainly do believe in Christ) rather, is this claim tenable or even seriously considered among academics and scholars? What are the greek epistles Josephus mentions?
"Epistle" is Greek for "letter". At the time, the only long-distance communication was by letters or messengers and the writing of eloquent and persuasive letters was a highly developed form of literature. The New Testament epistles use the conventions of that genre, and are the best-known examples in the present day, but thousands of other epistles have survived.
As Roman Emperor, Nero naturally had secretaries responsible for his correspondence. He would have used Latin for the western parts of the Empire, and Greek for the eastern. He would want a Greek secretary who was a native speaker of the language, so that his letters could be well-written and convincing.
The story Josephus is telling is about Burrhus, Nero's Greek-language secretary, who was bribed by Syrians in Cesarea to write a letter removing the equality under the law the Jews had in Cesarea. Burrhus had to get Nero's agreement to this, but Nero does not have a reputation as a careful administrator, so the agreement may well have been based on inadequate information. Giving individuals vast executive power tends to enable this kind of abuse.
I can't see anything in the passage from Josephus that indicates that Burrhus or Nero had anything to do with the New Testament epistles. Such a theory would have to be based on the wrong idea that "epistle" is very specific to the letters in the New Testament, in purpose as well as form, plus a mis-reading of the old-fashioned English in this translation.