The Tralfamadorians do not place much stake in free will; instead, they maintain that each event just is, that we are all like “bugs in amber”—that there is no “why.” This would seem to mean that none of us has a choice; as Billy says later, “Everything is all right, and everybody has to do exactly what he does.”
Billy’s and the Tralfamadorians’ opinions on free will are not, it would seem, analogous to Vonnegut’s, as Tyler pointed out earlier. He includes the Serenity Prayer, for instance, which clearly appeals to God for help differentiating between what can, and what cannot be changed—and changing those that can. Judging by this, it would seem that Vonnegut does see that not all situations can be changed—e.g. being abducted by aliens—but that we do have free will and can change our own courses of action.
Additionally, this passage would have me believe that Vonnegut wants to insiste that free will is not only existent, but necessary:
The doctors agreed: [Billy] was going crazy.
They didn’t think it had anything to do with the war. They were sure Billy was going to pieces because his father had thrown him into the deep end of the Y.M.C.A. swimming pool when he was a boy, and had then taken him to the rim of the Grand Canyon.
By denying Billy his autonomy at such a young age, his father has effectively denied him any sense of control over his own life or actions. We see Billy throughout the book, then, as a weakling, as a pathetic child and later, a pathetic man, who does not take action for himself. In the war, he is dragged around, yelled at, beaten, made fun of—yet none of this provokes him. After the war, he becomes an ophthalmologist simply because he is thrust into the field.
His lack of desire to even preserve his own life is a real sickness that seems to be directly cause by the removal of his free will—by his father, the war, the Tralfamadorians, his daughter. I think this is why he seems to be—to me and Ronald Weary, at least—repulsive. Though the robbery of his autonomy was nothing he could control (being that it was in the past), there is still so much Billy could change, if he wanted to: the present and the future.