The fact that Poe decided to call his plague "The Red Death" may not have been intentionally paradoxical. He may have simply wanted to avoid having the reader assume that he was writing a story about the so-called Black Plague. His story is more symbolic than historical, although there were actual instances where privileged people fled to the country and isolated themselves as a means of escaping the ravages of the Black Death. Giovanni Boccaccio's Decameron is a collection of stories supposedly told by a group of aristocrats who are entertaining one another while hiding out from the Black Death. Jack London wrote an interesting short novel titled "The Scarlet Plague" in which a plague which causes symptoms similar to those described by Poe wipes out nearly the entire population of the earth. It is a fascinating story and deserves to be better known.
In Edgar Allen Poe's "The Masque of the Red Death," the disease appears more allegorical than literal. There is obviously a literary connection with the Decameron, by Boccaccio, which describes a group of aristocrats entertaining themselves in the country whole trying to avoid the Black Death. The name of Prospero, and his function as a sort of stage manager of the retreat, also suggests Shakespeare's Tempest, and a sort of magical or unreal allegorical setting. As London was born after Poe's death, that is an unlikely influence. The four horsemen of the Bible would also be a possibility, but the red horseman symbolizes war, and pestilence is probably symbolized by the white horseman. Thus we can probably consider "red" as chosen simply as the color of blood.
The obvious paradox is that blood is a sign of life, in that living creatures survive by having blood circulate, and yet in the case of this disease, blood becomes a sign of death. There is also the paradox that the retreat designed to keep death out traps the visitors in with death.