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In The Prestige (2006), there is a magic trick in which a bird is made to disappear and it is revealed that the bird is secretly killed by crushing it flat to make it "disappear". Is this trick from real history, or was it invented for the book/movie.

It is based on a real trick, but the sources I provided do not conclusively state if any birds in these acts were ever killed. Only rumors and at least one inquiry, resulting in no substantial proof.

It appears the general nature of the trick in The Prestige is a variation of the real life, Vanishing Bird Cage:

The vanishing bird cage, also known as the flying birdcage, is a
classic parlour magic effect that was invented by French magician
Buatier De Kolta. The trick has also been used by magicians Carl
Hertz, Harry Beardmore, Harry Blackstone (Sr. and Jr.) John
Mulholland, John Angel, Sabrina Vera, and Tommy Wonder.

The magician displays a bird cage, holding it between both of his
hands. The cage is rectangular, about six inches tall by six inches
wide by eight inches long, and made of wire on all six sides. Often
there is a bird, though in modern performances of the act it is
usually fake, inside the cage. The magician will offer the cage for
inspection by an audience member, but he will never actually release
his grip of it. Then, without covering the cage, the magician makes a
sudden motion and the cage (and anything inside) vanishes from sight.
A variation of the trick was featured in the 2006 film The Prestige.

More Information:

The Vanishing Birdcage was a sensation and was also quickly ripped
off. In the Summer of 1875 Harry Kellar is said to have purchased a
cage from DeKolta's cousin for $750. Of course this was unauthorized
because Buatier never sold cages to anyone. This cage was probably
the very first one outside of DeKolta's act, but it wouldn't be the
last. In fact, Harry Kellar can probably be credited for the deluge of
Vanishing Birdcages in America because he sold the secret to a magic
dealer in exchange for props. In Europe a letter from Robert Heller to
Charles DeVere the french magic dealer shows that the cages were
already for sale in December 1875.

Harry Kellar stirred up a bit of controversy while in Australia over
his presentation of "The Flying Cage" as he called it. Harry Kellar's
routine was simple and direct, he counted to three and the cage with a
live canary inside would vanish! A rumor circulated that Kellar was
killing a canary every time he presented the effect. An inquiry took
place and Kellar proved that was not the case. He showed that he had
one bird and one bird only that he had been using for a long while.
But this same controversy would come to haunt other magicians across
the globe. In fact, this controversy was used as a minor plot point in
the movie "The Prestige" in which they give a rather fictitious
explanation on how the cage works.

I did a little research on this question and it appears that the trick MIGHT kill the canary, or might not, but inevitably did result in a lot of bird deaths. Here is the notice:

The vanishing bird trick (which, I regret to say, kills a great number
of canaries) is performed by means of accessories in which the costume
plays a part. The bird cage itself is made to collapse into a cigar
shaped tube. The centre of the cigar shape is naturally fatter than
the ends, and, if the bird is fortunate, it is secreted there and may
come out of the ordeal alive. Should, however, the bird get at either
end it is crushed to death, or should the legs get through the bars
they are almost certain to be broken. A conjurer once told me he had
done the trick 200 times with one bird, but I should very much doubt
it. What happens is this. The bird cage is rapidly hooked to the end
of a piece of whipcord, which passes up the sleeve and across the body
of the performer, and then down the other sleeve, where it is tied to
the wrist. It will thus be seen that the cord is considerably shorter
than will be required to stretch from each end of the arms if they are
extended. The cage, being in the performer's hand, is rapidly
compressed and made to assume its cigar shaped form, and is dragged up
the arm at lightning speed by the simple process of extending the two
arms. This very simple trick has puzzled millions of people. It is
performed so rapidly that even if you closely watch the conjurer I
doubt if you will know what he is doing. Afterward the conjurer
usually pretends to find the bird among the audience. As a matter of
fact he takes another bird out of his pocket, and by one of the simple
dodges of conjuring appears to take it from some one's neck or head,
or some other convenient place. -- Current Literature 1893