From the moment Sam and Bill kidnap Johnny Dorset, he terrorizes Bill nonstop, which causes Bill a significant amount of distress, anxiety, and pain. Johnny Dorset, who prefers to be called Red Chief, is an imaginative, rambunctious child. He physically abuses Bill by attempting to scalp him, dropping a red-hot boiled potato down the back of his shirt, and firing stones at him using a homemade slingshot. After Sam heads into town to deliver a ransom letter for Johnny's return, he arrives back at the camp, and Bill explains to him how he could no longer endure being around Red Chief. Bill proceeds to apologize for abandoning their plans of attaining the ransom money and tells Sam that he dragged the boy down the mountain and left him on the road headed towards Summit. After Bill tells his story, Sam asks,

"Bill . . . there isn’t any heart disease in your family, is there?" (Henry, 13).

Sam then tells Bill to turn around, and he sees Red Chief standing behind him. Sam's question is a humorous comment, which implies that Bill will have a heart attack whenever he discovers that Red Chief followed him back up the mountain.

The brief answer is that Sam does not want Bill to have a heart attack (or at least he is acting as if he is worried that Bill will have a heart attack).  So he asks Bill if anyone in his family has had heart disease before he tells Bill to turn around.

The point of this line is that "Red Chief" has been torturing Bill ever since Sam and Bill kidnapped him.  He has bitten and kicked Bill and made him eat grass, among other things.  At the point in the story where Sam asks about heart disease, Bill thinks that they have finally gotten rid of the kid.  But they have not -- Red Chief is right behind Bill.

Sam knows this will not make Bill happy and that fact is emphasized by Sam asking Bill about the heart disease.  The author has put this line in here to be funny and to stress how much Red Chief has made Bill's life miserable.

In "The Ransom of Red Chief," why does Bill ask Sam the following?: "There isn't any heart disease in your family, is there?"

Actually it is Sam who asks Bill the question. Here is the pertinent dialogue from the story.

“Bill,” says I, “there isn’t any heart disease in your family, is there?”
“No,” says Bill, “nothing chronic except malaria and accidents. Why?”
“Then you might turn around,” says I, “and have a look behind you.”
Bill turns and sees the boy, and loses his complexion and sits down plump on the ground and begins to pluck aimlessly at grass and little sticks.

Bill is the one who is stuck with Red Chief most of the time. He thought he had gotten rid of the boy by treating him roughly and sending him back home to his father. But Sam sees the boy returning from behind Bill and is a little afraid of alarming him by warning him of Red Chief's approach. At the same time he feels he needs to warn him because they never know what the boy might be planning to do next. That is why he asks, in a semi-humorous fashion, whether Bill has any heart disease in his family. He thinks Bill might have a fatal reaction to the shock. The biggest problem these would-be kidnappers have in the entire story is controlling their victim. Red Chief makes victims out of Bill and Sam, especially out of Bill, who has to act as custodian while Sam is negotiating with the boy's father and running other errands.

A very short while later they receive a reply to their ransom letter. Not only are they stuck with Red Chief but his father wants them to pay him $250 for taking the boy off their hands. This is the ironic situational twist on which the story is built. Bill and Sam have had so much trouble with their victim that, as Ebenezer Dorset expected, they are willing to accept his terms.