John Silver and Jim Hawkins did not expect to be close friends throughout the duration of the expedition. Jim was not especially estatic about being his cabin boy and John Silver felt that Jim would be a burden on his shoulders. Later on, though, Silver talks to Jim after preventing him from being harmed by the pirate crew.

Silver: "Didn't your pap ever teach you how to pick your fights a bit more carefully?"
Jim: "No."
Silver: "Your pap wasn't the teaching sort?"
Jim: "No, he was more of the taking-off-and-never-coming-back sort."

In the Junior Novelization, it mentions that Silver felt some connection with Jim there because he reminded him of himself as a young lad. He had discovered that the most reliable remedy for loss and pain was work, so he assigns Jim a series of chores to accomplish the following day(s). Eventually, each of them had developed a friendship with each other; Jim saw Silver as a sort of 'substitute father' and Silver had treated the adolescent as a son of his own.

However, I felt that there was one brief yet powerful scene that confirmed their bond with one another. During the supernova scene, when Silver was about to be blown away by the fierce winds of the explosion, Jim's eyes widen as he yells, "Silver!", immediately reeling him back with a rope that was fastened around him. It may be just me, but the anguished, panicking tone in his voice just made all the difference. Yes, it was brief, but it gave us a great demonstration of their relationship with each other.

The, of course, there was the speech that Silver gave in an endeavor to reassure his friend when he was accused of being responsible of Mr. Arrow's death.

Silver: "It weren't yer fault, ya know. Why, half the crew would be spinnin' in that black abyss if not for --"
Jim: "Look, don't you get it? I screwed up! For two seconds, I thought that maybe I could do something right, but I just … just forget it."
Silver: "Now you listen to me, James Hawkins! You got the makings of greatness in ya! But ya gotta take the helm and chart your own course. Stick to it, no matter the squalls. And when the time comes, ya get to really test the cut o' yer made of … well, I hope I'm there, catching come o' the light coming off o' ya that day."

Silver tries to hide the fact that he's grown a soft spot for 'Jimbo' by telling the pirate crew that all he cared about was finding Flint's treasure trove. Jim is heartbroken and believes that he had been duped by Silver. Even though Jim had damaged his robotic leg, Silver couldn't bear to harm him. In the end, he surrenders his one lifelong obsession -- the one that had taken away half of his body and probably most of his life -- in order to rescue Jim from falling into a vast river of molten lava.

The two of them share an inseparable bond and learn that friendship was of much more value than the riches of a thousand worlds.

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