In the 14th century the disease began its spread in central Asia, and eventually made its way to Europe - where it was estimated to have killed between one and two thirds of Europe's population. In total the Black Death was estimated to have taken 75 million lives.
The immortal being Flint was in the Earth city then known as Constantinople when the Black Death came to the area. Rodents, rats to be specific, were carriers as they infested the city. (TOS episode: "Requiem for Methuselah")
In 2267, it was feared that Mickey, a rat that Hikaru Sulu had brought on board the Enterprise, was carrying the plague, and a shipwide search was begun for him. Kirk later deduced that this was a ruse on McCoy's part to prevent the crew from succumbing to space cafard. (TOS novel: Mission to Horatius)
In 2267 in an alternate timeline created by escaped asylum inmate Trangur, James T. Kirk, Spock and Leonard McCoy found themselves trapped aboard the Earthfleet USS Enterprise (NCC-2101). To get out of their situation, McCoy claimed that during their travels through Earth’s past Kirk had contracted the Bubonic Plague. Montgomery Scott immediately forced Kirk, Spock and McCoy off the ship at gunpoint to protect the ship. They beamed down to Gateway and were able to return to the prime universe. (TOS comic: "No Time Like the Past")
In 2270, Commander Spock observed that if he had used Doctor Georges Mordreaux's time travel device to go back to Hikaru Sulu's favorite period in Earth history, he'd be regarded as a heathen freak and given two choices on how to die. One would be through blood poisoning sustained when cut by a sword, and the other would be the plague. (TOS novel: The Entropy Effect)