The Will to Power
If Cloud Atlas were a simmering stew, Nietzsche's philosophies would be the spices. Quite a few characters name drop Nietzsche and a few use the phrase "will to power" verbatim—and it never seems to be a good thing. At least, it's not a good thing to people not in power. Alberto Grimaldi mentions will to power in the same speech in which he validates institutionalized slavery and defines power as "the ability to determine another man's luck" (3.29.2).
Morty Dhondt also mentions the will to power as a prelude to his speech that mankind's lust for power, knowledge, and violence will cause the end of the world. In case you skipped German Philosophy 101, take a look at this for a quick course on The Will to Power. Basic idea? People want to get the best out of life: they want the best position, best house, best mate, best everything they can get.
This can be a good or bad thing, depending on what each individual person wants. The will to power could be a search for knowledge and self-perfection, or it could be a drive to exploit and hurt other people.
Are the interpretations in Cloud Atlas in line with Nietzsche's philosophy?
The whole reincarnation, matryoshka-doll structure is informed by another Nietzschean trope: eternal recurrence. Go here for a crash course. The basic idea, according to Nietzsche, is that time is infinite and everything that happens in the universe will keep happening, over and over again. That burger you at for lunch? You're going to keep eating it, over and over again, in an infinite number of (probably identical) lifetimes. Um, great?
Frobisher is a big believer in eternal recurrence. Vyvyan Ayrs even names the composition they're working on Eternal Recurrence. As Frobisher puts it in the last letter before his suicide, "We do not stay dead long. […] Thirteen years from now we'll [Rufus Sixsmith and Frobisher] meet again at Gresham, ten years later I'll be back in this same room, holding this same gun, composing this same letter. […] Such elegant certainties comfort me at this quiet hour" (10.8.11).
Is eternal recurrence just a big honking do-over button? Would Frobisher have killed himself if he didn't think he were going to live again? Eternal recurrence isn't that simple. When traveling with Hae-Joo, Sonmi hears him utter the password "travel far enough, you meet yourself" (7.1.57). That could play into the eternal recurrence philosophy. If you meet yourself, do you like what you see? Is eternal recurrence meant to be a reward, a punishment, or a purgatory?