What is Kurt Vonnegut's tone throughout Slaughterhouse Five?

Concerning your question about Vonnegut's Slaughter-House Five, I suggest that the speaker's tone is detached understatement. 

You are certainly correct about sympathy being revealed by the tone, as well as by the content.  The result of reading a scene is that the reader feels sympathy for Billy, etc., but I think this is achieved with detached understatement.

Notice the "So it goes" refrain.  Somebody dies, a catastrophe happens--oh well, so it goes, that's life. 

Importantly, it's not that the speaker doesn't care, it's that there's nothing he can do about any of it.    How does one fight a fire-bombing? 

Understatement is an often-used, often highly effective literary device.  If a writer tries to write a death, for instance, by demonstrating how horrible and meaningful, etc., the death is, he/she can overwrite and be caught in the trap of trying to convince the reader of something, like in an argument essay.  Understatement lets the reader figure out the meaning, and the reader often fights for the meaningfulness of the death, instead of resisting it. 

The speaker distances himself from events, then, he does not get emotional.  He can't change anything, anyway.  He just tells it in a straightforward manner.  So it goes.