Answer:
1. (At the beginning of the story):
"There was a town down there, as FLAT AS A FLANNEL CAKE, and called Summit, of course." (a town as flat as a flannel cake - ie as flat as a pancake is an example of hyperbole/exaggeration because no town could literally be as flat as a pancake - but the author, O. Henry, exaggerates the flatness of the town to emphasise the irony of the name of the town "Summit" - which implies that the town should be hilly or on top of a hill.
2. I went out and caught that boy and SHOOK HIM UNTIL HIS FRECKLES RATTLED. ("shook him until his freckles rattled" is an example of hyperbole. The author uses this phrase to emphasise that he/Sam shook the boy vigorously. The boy's antics had driven Sam and Bill to drastic measures and so he emphasises their annoyance and irritation by painting an exaggerated picture of the boy being shaken - till his freckles rattled).
3. "You know, Sam," says Bill, "I've stood by you without batting an eye in EARTHQUAKES, FIRES AND FLOODS -- in poker games, dynamite outrages, police raids, train robberies and cyclones. I never lost my nerve yet till we kidnapped that TWO-LEGGED SKYROCKET of a kid. (The hyperbole of "earthquakes, fires and floods" and the metaphor "skyrocket" are used here as a contrast. Bill says that he has stood by Sam throughout almost everything possible and uses exaggeration/hyperbole "earthquakes, fires and floods" etc to emphasise this point and then says that this is nothing compared to dealing with this "two-legged skyrocket of a kid". Obviously, the boy is not a skyrocket but the use of hyperbole in this sentence helps the reader to imagine how wild the boy is and how difficult it is for Sam and Bill to deal with him.)
4. "Sam," says Bill, "I suppose you'll think I'm a renegade, but I couldn't help it. I'm a grown person with masculine proclivities and habits of self-defense, but there is a time when all systems of egotism and predominance fail. The boy is gone. I have sent him home. All is off. There was martyrs in old times," goes on Bill, "that suffered death rather than give up the particular graft they enjoyed. NONE OF 'EM EVER WAS SUBJUGATED TO SUCH SUPERNATURAL TORTURES AS I HAVE BEEN. I tried to be faithful to our articles of depredation; but there came a limit." (The hyperbole here is "None of 'em ever was subjugated to such supernatural tortures as I have been." This exaggeration of the boy's behaviour and claiming that it is worse than anyone has ever experienced emphasises just how difficult they think the boy is to deal with and just how desperate Sam and Bill are to get rid of him.)
5. (At the end of the story when the boy's father is holding him back so Sam and Bill can get away):
"How long can you hold him?" asks Bill.
"I'm not as strong as I used to be," says old Dorset, "but I think I can promise you ten minutes."
"Enough," says Bill. "IN TEN MINUTES I SHALL CROSS THE CENTRAL, SOUTHERN AND MIDDLE WESTERN STATES, AND BE LEGGING IT TRIPPINGLY FOR THE CANADIAN BORDER."
(It's definitely not possible for someone to travel this distance in 10 minutes whether it be by foot, car, train, airplane etc but the hyperbole shows how desperate Sam and Bill are to get away from the boy.)