The etymology of the phrase is traced back to Aurthurian Lore. Huckleberry Garlands were said to be given to Knights of the Kingdom for coming to the service of a damsel. They would approach the lady, lower their lance, and receive the small branch as a symbol of gratitude; much like a medal.
Therefore, "I'm Your Huckleberry" literally means "I'm your Hero."
In current adaptaions, in reference to the movie Tombstone, it means "I'm your man." as an affirmative response to a challenge.
Wretched slugs, don't any of you
Have the guts to play for blood?
I'm your huckleberry.
Ringo turns. Doc stands there, smiling that Cheshire cat
That's just my game.
Taken form the offical script from the movie Tombstone.
"No one can beat me in COD 1 on 1"
"I'm your Huckleberry."