Asking about Kurt Vonnegut's purpose in writing Mother Night presumes two things, first that we can fully know the interior thoughts of an author (or any other person!) and second that the author's intentions should affect our reading of the book.
Kurt Vonnegut's explicit statement about the book, that it has a moral but he doesn't know what the moral is, suggests that this is not a work written for a distinct and singular purpose in the way, e.g. Carson's Silent Spring could be said to have been written to stop the use of DDT. Since Vonnegut is a professional writer, one motivating factor was probably making money. Because his work tends to ludic postmodernism, we can also see it more as an exploration of ironies and ambiguities than having a singular point.
The New Critical theory of the "intentional fallacy" and later postmodernist theories proclaiming the death of the author both argue that authorial intention should not be used as a guiding principle in interpreting texts.