Barthelme's most anthologised story 'The Indian Uprising' works like allegory, where 'Indians' stand for all the other races that the US have oppressed (especially, in 1968, when the story was published, the Vietnamese). It's also like allegory in the apparent randomness of many of its references, but where the associations become surreal.
That story isn't all that representative, though, because it's not funny as so many of Barthelme's stories are. I was just reading 'The King of Jazz' and the self-consciousness about language there reminded me of certain stand-up comedians. Stewart Lee in one of his books talks about the comic value of certain words like 'wool' for example. But one of his comic effects is based on being exaggeratedly articulate and wordy, and, when Barthelme describes an especially effective piece of jazz playing he does something similar when he says that it 'sounds like the cutting edge of life...like fumaroles smoking on the slopes of Mt.Katmai...like an oyster fungus growing an aspen trunk...like a mule deer wandering a montane of the Sierra Nevada...like coatimundis moving in packs across the face of Arkansas...