For example, after Dmitri is arrested for the murder of his father, the police interrogate him. Grushenka rushes into the room, begging that she be punished for her role in Dmitri's downfall:
“Judge us together!” Grushenka cried frantically, still kneeling. “Punish us together. I will go with him now, if it's to death!”
“Grusha, my life, my blood, my holy one!” Mitya fell on his knees beside her and held her tight in his arms. “Don't believe her,” he cried, “she's not guilty of anything, of any blood, of anything!”
He remembered afterwards that he was forcibly dragged away from her by several men, and that she was led out, and that when he recovered himself he was sitting at the table. Beside him and behind him stood the men with metal plates. Facing him on the other side of the table sat Nikolay Parfenovitch, the investigating lawyer. He kept persuading him to drink a little water out of a glass that stood on the table.
Our glimpse of the future amounts to a vague image of Dmitri looking back on the present. We don't know what he's doing at this future time, whether he's in prison, or free and settled with Grushenka--only that he's alive, and capable of remembering. We don't know how far in the future we are, either; it might only be a few minutes. We don't even know what Dmitri makes of this memory. Is he amused, remorseful, at peace? What is the point of this sudden shift in perspective?
While seeming to provide concrete information (Dmitri will not die, at least not in the next few moments), this move deepens the sense of mystery overall by raising all sorts of additional questions. It also reminds us that there's a narrative intelligence outside of Dmitri, who knows the future--the anonymous first-person narrator, who is more evident at some points than at others. Here he doesn't announce himself directly, but sort of ripples the curtain between us and the story, making us aware of that curtain at a moment of absorbing drama. The characters are engaged in intense dialog--and in dialog, characters can seem especially real and autonomous, as they speak in their own words, rather than being described by the author's. The flash-forward, however, makes them fictional characters once again, if only for a second. Perhaps the (also fictional) author-persona just can't resist making his power known; he's a terrible egoist in his way, and can't let these fakers run away with his tale. Or maybe we're learning that while Dmitri may not be doomed by this investigation, he's doomed in a larger way by his author-God--just as we all are.
Should we, as apprentice writers, attempt such flash-forwards? They clearly mess with your reader's ability to get lost in the story. However, I, for one, like the artificial effects it creates. (I call it "making my stories less publishable.") It's also a way of announcing--if you feel you need to--that your fiction is literary. When Joyce Carol Oates read her story "The Knife" at Stanford last fall, an audience member asked her why she'd employed a flash-forward during the scene in which the main character's life is being threatened. The flash-forward tells us everything is going to be (more or less) OK, which, to the questioner's mind, destroyed the suspense. With the breezy contempt for which Oates is celebrated, she explained that this was not a suspense story.
The flash-forward, if done well, frees you as the author to do other things with a conventional, if gripping, narrative. The question is whether you want to sacrifice that kind of hold on your reader in favor of other ambitions. We know that in the end, Dostoevsky really wants to talk about God, not bicker and argue about who killed who. There's a larger matter at stake than either Dmitri's or his father's life.