There are multiple possible answers to this. I’m your Huckleberry shirt. But one common belief is that the term “huckleberry” is idiomatic. It was made famous by John “Doc” Holliday and originates from his home state of Georgia. It was likely a corruption of the term “hackle bearer.” Hackles are the handles on the side of a coffin. Thus, the statement, “I’ll be your huckleberry” means, “I’ll still be around when you’re dead.” There is a great answer to this at World Wide Words: Huckleberry. I am not affiliated with this site in any way. And found it by Googling the sentence, “I’ll be your huckleberry.”
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This line became famous when Val Kilmer’s Doc Holiday said, “I’m your huckleberry” to Johnny Ringo in reply to Ringo’s challenge of Wyatt Earp in the movie Tombstone. The context suggests that the declaration means that the person saying it is willing to do what the other person is requesting or demanding. This seems to be the meaning many ascribe to the statement. In the movie, it means that Holiday is willing to accept Ringo’s challenge to a gunfight, with the intention of killing him. Huckleberry is a character.
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From Mark Twain’s literary world of the ‘Adventures of Tom Sawyer’. I’m your Huckleberry shirt. As a character, he is the close companion of the main protagonist. The phrase is used to highlight the friendship between a pair of associates. It was a pretty commonly used term in the South. There’s been a lot of discussion over the meaning ever since Val Kilmer uttered it in the film. Basically “I’m your huckleberry” means “Name the place. And I’ll go with you,” “Name the job and I can do it,” “I’ll oblige you” or “I’m your man.”