Kiwi asks…
What does "My Huckleberry Friend" refer to?
Answer from a Native speaker

Rebecca
As a child, Johnny Mercer, who wrote the lyrics liked to pick huckleberries (which are a kind of wild blueberry) in the summer. To him, the berries had a personal link with his childhood, and he also liked the association with Mark Twain's character Huckleberry Finn. The lyric was meant to imply that the character, Holly Golightly, who was actually not as refined and upper class as she pretended, and Huckleberry Finn could well have been friends, if ever they had met. He wanted to link her character to the characteristics of Huckleberry Finn.
Listening Quiz