In the movie Tombstone, Val Kilmer gives a brilliant delivery of the line
I'll be your huckleberry.
I cannot remember any dialogue leading up to it that explained this retort. Was there any or is it a symbolic phrase?
The Dictionary of American Slang defines this, and supplies just this line from Val Kilmer in Tombstone as an example of its usage.
"I'm your huckleberry" means "I'm just the man you're looking for!"
"I'm your huckleberry..." Val Kilmer as Doc Holliday in Tombstone
Also, the podcast A Way With Words from Public Radio, is a call-in show about linguistics, and answered this question this way:
What it means is easy enough. To be one’s huckleberry — usually as the phrase I’m your huckleberry — is to be just the right person for a given job, or a willing executor of some commission. Where it comes from needs a bit more explaining...
The accepted answer explains the phrase very well. As to the other part of your question - what dialogue leads up to Doc Holiday/Val Kilmer uttering that phrase:
What leads up to it is Ringo, a very deadly guy, is drunk and itching for a fight.... a potentially lethal one. Others, of course, are not interested, and, I believe, Wyatt Earp is doing all he can to de-escalate the situation at the tables, which only infuriates Ringo more, since he has no outlet for his desire to fight and/or kill.
He then says -
Wretched slugs, don't any of you have the guts to play for blood?
To which Holiday replies that he's willing to play that deadly game with the phrase you are asking about.