Can a novel chapter have a suspenseful flashforward opening?

Not a "suspenseful" opening perhaps, but here are the opening paragraphs of To Kill a Mockingbird:

When he was nearly thirteen, my brother Jem got his arm badly broken at the elbow. When it healed, and Jem’s fears of never being able to play football were assuaged, he was seldom self-conscious about his injury. His left arm was somewhat shorter than his right; when he stood or walked, the back of his hand was at right angles to his body, his thumb parallel to his thigh. He couldn’t have cared less, so long as he could pass and punt.

When enough years had gone by to enable us to look back on them, we sometimes discussed the events leading to his accident. I maintain that the Ewells started it all, but Jem, who was four years my senior, said it started long before that. He said it began the summer Dill came to us, when Dill first gave us the idea of making Boo Radley come out.

The whole rest of the novel is a telling of the "events leading to his accident." Said accident happens right at the end of the story (by which time, I suspect, most readers have completely forgotten about it!)

Yes you can.

It is actually quite a well used device in SF and Fantasy (books, although they obviously do it in tv shows too) with long build-ups, to start with an action scene from later as a opening for the book or a section/chapter. This hooks the reader and keeps them reading when they may otherwise find the book slow to get going.

The term I've mostly seen used for this is flash-forward.

The type of thing often used is the main character in the middle of a fight for his life, in a cell awaiting execution, on a derelict space ship with the air running out, hiding from pursuit in a forest and hearing the baying of hounds coming closer, etc. Just before something final happens, the story segues into the actual chapter, usually with some sort of "flashback" device at the end of the prologue along the lines of: I can't belive that bastard sold me out ... ; I should never have taken this job ... ; and to think, just a week ago they wanted to crown me king ... ; Things have certainly come a long way since ... Earlier that morning ...

My Sister's Keeper starts with a prologue a few hundred words long. A nameless girl writes how, when she was three years old, tried to smother her sister with a pillow. However, her dad stopped her from going through with it. She writes how later in life she kept fantasizing about killing her sister, but the prologue ends with this statement:

In the end, though, I did not kill my sister. She did it all on her own. Or at least this is what I tell myself.

As a reader we don't even know any of the characters' names yet, but the author already spoils the ending. Somebody will die by the end of the book, either a murder or a suicide.

In chapter one we are introduced to Anna, who seeks the help of a lawyer to sue her parents. Anna's sister Kate has a rare form of cancer and her kidneys are failing and their parents want Anna to give up one of hers.

Throughout the story we learn Anna was born with a purpose. A genetically-screened test tube baby, the blood in her umbillical cord was used in an experimental therapy to extend Kate's life. Extend, not cure. And what started as a one-time sacrifice quickly becomes a regular occurrence. She's forced to give up blood and bone marrow, and has to take growth hormones even though she's not sick. Meanwhile she can't live a life of her own, and we, the reader, realize this circle of pain will keep going on until Kate dies.

The lawsuit unfolds, and we learn something new. Anna sued her parents on Kate's behalf. Instinctively we understand the events of the prologue are approaching rapidly. We will catch up with the here and now soon enough, the consequence chiseled in stone. Anna will win, gaining a life of her own at a terrible cost.

Except...

The twist ending is maybe ten pages long, and although the story would suffer thematically, you could cut off the end and still have a functioning book. In fact, the author could have signed the prologue with Kate's name and it wouldn't have mattered. Why? Because we don't read to get to the conclusion. Rather than the suspense of 'how will this end,' the book's true strength is the palpable tension which exists between all of the characters.

Anna struggles against her parents for bodily independence, for the right to have her concerns be heard. She struggles against herself, torn between not wanting Kate to die and respecting her wishes. Between doing what's right and keeping the family from burning down. Her parents struggle with feelings of powerlessness, of clinging to false hope, the realization they've neglected their other children. The book's conclusion has no influence on any of these sources of tension.

Yes. You can start a story by giving away the ending, given you substitute mystery with tension. I think My Sister's Keeper is still a compelling read, if you can't tell by my screenname.

If you can get the reader to go along with your scheme, you can put any scheme into place. The question then becomes, what does the reader require to make going along with the scheme the best choice?

I would guess that the key issue is what you as the writer chose to reveal. If you go too far ("the butler kills John with a fire poker in the library at Raven's Point"), some of your readers are going to bail immediately. Of course, if you as the writer have the skill to engage the reader by raising questions that your foreshadowing does not quite answer, you might keep some of those readers. Wait, is this the same butler that two chapters ago fell off the cliff into the storm-tossed ocean? And didn't John swear that he would die before he set foot in Raven's Point ever again? Perhaps you only reveal that the butler swung the fire poker with the suggestion that the poker struck something.

One thing to keep in mind is that a standard technique with foreshadowing is that you as the writer should seek to misdirect the reader. Here are four facts but only one of them makes a difference by the end of the story and not in the way that the reader might assume it might make a difference. Perhaps, John in the foreshadowed scene is really Jim, John's evil twin, trying to cash in on an inheritance due John (who is off in darkest Africa saving the world). Perhaps, John has a steel plate in his head (or the hat that he is wearing) that protects his brain. Perhaps, ....

What you need after you put all of this together are beta readers who will tell you the truth. These beta readers should be representative of the intended audience for the story. You should plan to revise the story several times to get the shading of the foreshadowing just right.