The most significant conflict from the first fifteen chapters is the one that pits Huck against his father. Huck is abused, verbally and physically, by his drunken father, Pap Finn.
Pap wants to take over the upbringing of his son and find a way to get Huck's money. Huck is endangered by his father and so must escape from him.
This external conflict leads Huck to devise a plan to fake his own death and head down the river.
An internal conflict that appears in these early chapters relates to Huck's moral dilemma. When Huck meets Jim on the island and hears Jim's story, he realizes that he is going to have to choose sides. He wil either side with Jim, keeping his secret and helping his run away, or he will side with "society", agreeing with its laws and morals and turning Jim in.
Huck is divided about what the right thing to do is in this situation. He chooses to side with Jim but remains conflicted.