One of the central conflicts of this novel relates to Huck Finn's conscience.

Huck's main struggle in the book is with his conscience, the set of morals with which he has been raised.

This is an internal conflict (we might see his repeated crises of conscience as a single conflict or as a series of conflicts). The outward conflicts in the novel almost all become fused with this internal conflict, in one way or another. 

Huck's internal conflict can be expressed as a struggle to navigate two types of morality - a natural moral instinct and a learned moral code. Huck's moral instinct is repeatedly at odds with his moral instruction. He finds that many situations offer him no good outcome. His conscience will haunt him no matter what he does. 

Huck has a difficult time understanding that the social norms he has received as dictates are no more of a guide to right behavior than his own natural instincts regarding morality.  

We see this internal conflict of conscience matched by an external conflict when Huck has to decide whether or not he will help Jim run away and then later escape captivity. 

On their trip, Huck confronts the ethics he has learned from society that tell him Jim is only property and not a human being. By this moral code, his act of helping Jim to escape is a sin.

Jim's captivity is an external conflict, or becomes one when Huck decides to help Jim escape.

Other external conflicts stem from Huck's affiliation with the King and the Duke. With these two, Huck has to decide how loyal he should be to these two swindlers. He cannot bring himself to betray them until they have already betrayed him.