Simon's conflict is between what he has to say, and the way he expresses it. Simon understands the true nature of the boys' fear on the island, and the fact that the beast is not really a physical presence on the island, but the evil inside the boys themselves. On the other hand, Simon's social shyness and lack of confidence mean that he is unable to express this finely-tuned understand to the rest of the boys:
Simon felt a perilous necessity to speak; but to speak in assembly was a terrible thing to him.
“Maybe,” he said hesitantly, “maybe there is a beast.”
The assembly cried out savagely and Ralph stood up in amazement.
“You, Simon? You believe in this?”
“I don’t know,” said Simon. His heartbeats were choking him. “But. . . ”
The storm broke.
“Take the conch!”
“Hear him! He’s got the conch!”
Simon actually finds it very, very difficult to speak in front of the other boys, even to express himself. In fact, Golding has to express what he thinks in the narration - as he never actually manages it in the assembly:
“What I mean is. . . maybe it’s only us.”
That was from Piggy, shocked out of decorum. Simon went on.
“We could be sort of. . . ”
Simon became inarticulate in his effort to express mankind’s essential illness.
This is the conflict: Simon's shyness and unwillingness to speak, against what he actually has to say. Which is what makes his death more ironic: he's decided to descend the mountain in order to tell the other boys what he knows about the "Beast From Air". And they kill him.
Simon's conflict is a spiritual and philosophical conflict. He tries to show the group that they are losing their good qualities and becoming bad uncivilised wild-things, that they are the beast. He struggles for the truth and what is right. In the end he dies for his brave stand against what he believes is wrong.