Suspense is generated when someone in a story – whether it's the main character or the narrator or both – knows something that we, the readers, do not. Usually this information is fed to us in small chunks to keep us hooked and waiting for more. The narrator of Kidnapped does indeed know a lot that we don't know – everything, in fact, since the story is told from his point of view after the events of the novel have occurred.
The narrator frequently uses foreshadowing: he implies something that's going to happen further along in the story to increase our curiosity. For example, when Davie is shipwrecked on Earraid, he tells us: "The time I spent upon the island is still so horrible a thought to me, that I must pass it lightly over" (14.10). In other words, the next chapter of the story is going to be filled with terrible tales of hardship. This kind of storytelling gives a strong emotional depth to the novel; nothing happens without Davie telling us how he felt about it.
At the same time, this foreshadowing hooks us and leaves us wanting more. How can we pass up these tantalizing hints that the story to come is "so horrible [...] that [he] must pass lightly over?" This way of narrating the novel piques our curiosity. With each new disaster, we just have to know how Davie's going to escape – especially since we know that he will somehow succeed or else he wouldn't be around to tell his own story.