DK is referring to a legendary clairvoyant of the 12th century, sometimes called "St. Malachy" (to distinguish him from the Hebrew prophet, Malachi).
Prophecy of the Popes - Wikipedia, the free encyclopedia
St. Malachy is said to have had a vision of 112 future popes, extending to the end of the world. The final paragraph of his vision reads as follows:
UTTER SPECULATION ON MY PART: whomever is elected as the next pope will be said by some to fit the prophecy on the ground that
all popes succeed from Peter in Rome and Malachy was using a symbolic name for the last one. Per Wikipedia, the Church itself thinks the "Prophecy of Malachy" is a forgery.