What we call the "Black Death" today, the plague epidemic c. 1350, isn't absent from late medieval English literature, of course. William Langland's Piers Plowman refers in its opening 'set the scene' to the "pestilence tyme" and resulting loss of population launching a new wave of abuses in Church finances. (For scale: if Chaucer is the J.K. Rowling of 14C literary culture, Piers Plowman is the Hunger Games trilogy.)

But you're right--Chaucer bases his storytellers' frame narrative on a pilgrimage to Thomas Becket's shrine at Canterbury, not citydwellers fleeing the Black Death like his probable model Boccaccio in the Decameron.

There are a few qualities of late medieval literary production and modern reception that can lend themselves to what might look like an absence of the Black Death from English literature. First, most of the most-read authors today come out of London clerk "reading circles", and can seem to be more wrapped up in more political issues of the day. Piers Plowman, for example, is more generally discussed in the context of the contemporary Peasants' Revolt of 1381. (Which, like the financial problems that Langland claims certain priests are claiming to have, is wrapped up in mostly-post-BD social changes).

Second, the sort of "historical fiction" that a late 14/15C author might set in such a recent, realistic time didn't really exist. Boccaccio finished the Decameron almost while Europeans were still burying the 1348-52 pestilence victims. Otherwise, there's the sort of (1) collapsing of history into the present--"King Arthur" is a late antique warlord...whose court looks exactly like a 12C, 13C, 14C, 15C court depending on when the particular text is written, right? or (2) clear setting in The Past, as with biblical or classical derivatives.

But the most compelling and, I think, interesting factor in play is the nature of pestilence in late medieval and early modern Europe. Today, we place all the emphasis on the outbreak that began in Italy in 1347. This tsunami had two key qualities: it was the first and it was the worst. Indeed, pestilence reoccurred frequently throughout the next several centuries. There were some especially bad and widespread years--1361 and 1481 tend to pop up in scholarship as particularly brutal for various reasons. But pestilence was almost never entirely absent from Europe; one city or another would have an outbreak at a given moment in time.

So while the memory of the "pestilence time" as 1348 clearly endured, as PP shows, pestilence fairly quickly also became a scary but omnipresent factor of life lurking in the background. And for the most part, each outbreak was a little less severe (scholars have raised various reasons such as better quarantine procedures, rising immunity among earlier survivors, evolution of the bacterium to be less deadly so as to ensure more reproductive time for it, and so forth). This would seem to contribute, over time, to a dulled sense of just how catastrophic, emotionally, that first outbreak was.

On the flip side, however, scholars agree that the recurring waves of pestilence, endemic warfare combined with wider knowledge of wars, plague, and other bad things across Europe from the late 14C, played a major role in stoking the culture of "dying well" that blossomed in late medieval religion and society. It's important to see the Black Death as catalyzing the entrenchment and popularity of the ars moriendi (art of dying [well]), not launching it. But you can't deny that the skeleton representing dancing death is all over late 14C and 15C European literature and art in a way it definitely isn't in earlier examples. Without reading the poem, I am positive the "Disputation between the Body and the Worms" comes out of this 'genre' or rather spectrum of genres--literature that deals in decay, decline, the gory earthy physicality of earthly life with a mortality limit in light of celestial eternity.

To a modern reader, this aspect of late medieval culture seems like a odd combination of resignation to the inevitable with the desire to control what little bit you can--that is, one's attitude towards the ultimate outcome of all life. Much of the ars moriendi plays out in religious literature--but then again, about 80% of 15th century literature was religious. And nearly all of that is quite terrible. Which brings us back to the original point: today, we read such a teeny, tiny sliver of late medieval literature.

For pretty good reason.