How would you characterize the tone of "A Hunger Artist"?

The tone of Franz Kafka's "A Hunger Artist" is so uncanny and at the same time so matter-of-fact that critics have invented a special name for it. The tone of this story is "Kafkaesque." It is very similar to the tone of some of his other stories, such as "The Metamorphosis" and "The Penal Colony." Reading a Kafkaesque story is like having a bad dream from which it seems impossible to wake up. Something horrible and nearly but not quite impossible is happening, but the description is so detailed and so "real" that it is undeniable. It is the unique tone of many of Kafka's stories, as well as at least two of his novels, that has called for the creation of the word "Kafkaesque." No doubt Kafka, like many European writers, was influenced by the bizarre tales of the great American poet and fiction writer Edgar Allan Poe. But Poe's tales seem relatively naive and wholesome in comparison with Kafka's neurotic nightmares. With Kafka's there is often a sense of despondency, hopelessness, and doom. They are also more like puzzles. The reader is left wondering what his stories "mean," whereas with Poe's stories the meaning is usually relatively obvious. Why would a man choose the profession of being a hunger artist confined to a cage like an animal? Why would other men keep any human being a prisoner in a cage? And why would people pay their good money to come in and stare at a man starving in a cage? 

How would you characterize the tone of "A Hunger Artist"?

Overall, the tone of this story can be characterized as fairly detached and unemotional.  The story is told in limited third person narration, that is to say it stands outside of the characters and events it describes while also giving us the intimate thoughts and feelings of one character.

This impersonal narrator relates the rather absurd story of the hunger artist in matter-of-fact terms. This is evident from the very beginning with the dispassionate observation about the decline of fasting as a form of popular entertainment:

In the last decades interest in hunger artists has declined considerably. Whereas in earlier days there was good money to be earned putting on major productions of this sort under one’s own management, nowadays that is totally impossible.

 As the story proceeds, however, the narrative does enter more and more into the mind of the hunger artist, so that his thoughts and feelings begin to colour the narrative tone, making it more personal and emotive. This is reflected in the quote below, when the hunger artist chafes against the fact that his manager always limits his fasting period to forty days at a time, as public interest tends to dwindle by that point:

Why stop right now after forty days? He could have kept going for even longer, for an unlimited length of time. Why stop right now, when he was in his best form, indeed, not yet even in his best fasting form? Why did people want to rob him of the fame of fasting longer, not just so that he could become the greatest hunger artist of all time?

The hunger artist’s indignation at this restriction on his art comes out clearly here in the form of a series of vexed questions.

In the main, though, as already stated, the tone of the story is coolly ironic, looking down on the somewhat ridiculous spectacle of the hunger artist, charting the public’s ever-increasing indifference and his dissatisfaction with his own art until his final decline and death. After describing his death in wholly unsentimental terms,  the narrative goes relentlessly on to recount how his cage gains a new occupant: a fiery panther whose fierce energy, noble beauty and pride contrasts most markedly with the emaciated, self-mortifying form of the hunger artist. Unlike its human predecessor, the panther proves to be a great draw. People genuinely admire this magnificent creature, as they never really admired the poor, misunderstood artist. The ironic narrative voice leaves us to contemplate this contrast and the whole rather grotesque tale of the hunger artist. We are left to reflect on artistic extremes, the gulf between the individual and society at large, the nature of public entertainment, and such-like themes.  

How do the events of "A Hunger Artist" align with its flat, matter-of-fact tone?

This is an excellent question. Of course, the point of view of this challenging short story is third person limited, which helps create the detached tone that you refer to. From the very start of the story, it is clear that the tone that is created stresses the normal, factual elements of "fasting" as a form of art:

During these last decades the interest in professional fasting has markedly diminished. It used to pay very well to stage such great performances under one's own management, but today that is quite impossible. We live in a different world now.

The story presents fasting as a now outmoded and anachronistic form of art that is no longer popular. However, to be taken in by this factual tone would be to ignore the very real element of humour that lurks behind this detached point of view. Of course, the hunger artist is presented as a figure of pity, but at the same time we cannot ignore the presence of the absurd. The notion that fasting is an "art" which is presented as an art form before admiring spectators is ludicrous. Likewise as we follow the struggle of the hunger artist to pursue his art to its highest and most purest form, we cannot escape the feeling that the hunger artist is a bit too self-important and places too much emphasis on his art. Kafka seems to be asking deep questions about the nature of art and the fervency with which we lead ourselves into states of artistic excess.