What is the conflict in The Acts of King Arthur and his Noble Knights?
The primary conflict in most Arthurian literature is the conflict between idealism and the human condition. This conflict is expressed in several ways in the Arthurian canon, though Sir Thomas Malory's Le Morte d'Arthur, and Steinbeck's retelling of it in The Acts of King Arthur and His Noble Knights, focuses particularly on the idealism versus the realities of chivalry.
The rules of knighthood (i.e., chivalry) were historical medieval codes of conduct for any man who represented the king in battle. Knights had to be both gentle and strong, noble and servant. Their motto, approximately, was "might for right," meaning that violence should only be used as a means to a virtuous end. Violence referred to physical violence but also referred to the violence caused by abusing one's power.
Steinbeck particularly wanted to show how aspiring to a virtuous life would take a toll on a person. Central to this theme is the romance between Lancelot and Guinevere, which threatens to undo all of the good Arthur and his knights have done in the kingdom. In spite of knowing the destruction their romance will cause, they cannot rise above their human desires and choose virtue.
When you say conflict, do you mean the role of King Arthur's noble knights? Life was very violent and even the church recognized the need for fighting. King Arthur would need to fight to keep his kingdom safe from constant invasion. The Knights of the Roundtable fought for Camelot, they fought for King and country.
"More than ever, war was thought of as a glorious adventure, a way to acquire wealth, honor, and prestige (status) while fighting in the name of God and the church against those who did not accept God's word."
A knight lived by the code of chivalry, loyalty to the king unto their deaths, to defend the king, to protect the weak and underprivileged, to be true to his lady love, and to seek adventure. Knights were champions of good, they were required to fight evil and injustice.
One of the other roles of the Knights was to seek the Holy Grail, which was literally interpreted in the Middle Ages to be the chalice, or cup that Jesus Christ used at the Last Supper.