Fear is absolutely a prominent theme in Lord of the Flies, but I’m not sure that Joseph Conrad’s book Heart of Darkness can really be considered a theme in Lord of the Flies. (Perhaps it could be considered an allusion.) However, the two books certainly share the theme of fear and savagery. Let’s look at those two themes using examples from the book in order to answer your question more thoroughly.
First, let’s look at the theme of fear. Probably the best example is the group of boys’ fear of the unknown that they represent visually as a “beast” on the island they inhabit.
Maybe there is a beast … maybe it's only us.
The irony is that the “beast” ends up being personified as a dead body, the corpse of a dead paratrooper in the fallout of the atomic wars, the boys simply do not understand what it is. As the story moves on, some of the boys fear the new, uncivilized nature of the group. In my opinion, this is best shown by the character of Simon. Simon finds a beautiful and hidden place in the jungle that none of the other boys know about because it is deftly hidden by a mass of creeper vines. Simon often flees to this place in order to escape the craziness of his tribe and think about the grandiose beauty of the natural jungle. What he is really fleeing is the beast that the tribe has become.
In regards to Conrad’s Heart of Darkness, there is a definite connection to descent into savagery as a theme. One can see this physically in the boys appearance as they continue to live on the uncharted island. When they first arrive, they are still adorned in proper British schoolboy uniforms; however, as they begin to get used to living in such a wild place, they become wild themselves. Their hair is unbrushed and unkempt. Their clothes are raggedy. Their shoes are discarded. This echoes Kurtz’s descent in to savagery found in the Heart of Darkness. Another example of this savagery is the decision to choose Jack (the roughest) as the eventual ruler over Ralph (the most realistic). The new tribe that chooses Jack’s leadership is the tribe that kills both Simon and Piggy.
Ralph wept for the end of innocence, the darkness of man's heart, and the fall through the air of the true, wise friend called Piggy.
In conclusion, the themes of fear and savagery are the two themes most closely related to Conrad’s Heart of Darkness. The boys have a grand fear of the unknown that manifests itself in the “beast” of the title. Further, they descend into savagery when they choose Jack over Ralph as their leader. Murder ensues and chaos reigns.