Vonnegut himself released it, in his book, Palm Sunday.
EDIT: Oh, you mean you took him literally, that he didn't even have his own copy. Well:
"And no copies of this letter have been sent to anybody else. You now hold the only copy in your hands."
It sounds like this could imply that he could be holding onto a copy himself. Interesting point, why would you do that if you didn't mean to exploit it, at least eventually? Or maybe he just likes to hold on to things for records.
It's obviously the most likely explanation but still, it perhaps stretches what might be considered usual for the period.
(Note to self: Don't skip the italicized, parenthetical text before an interesting piece of content)