1. Social integration (Facebook is a huge distribution channel). It might be a little spammy, but you could consider auto-posting stories to people's walls. 99% of the time people don't care (people on Hacker News form part of that 1%). I'm not sure how the social loop of your app works, but you can incorporate a "share with your friends" button that tells user's friends about the book.
2. Keyword optimization. Optimizing your keywords can net you up to a 2x boost in search rankings and downloads coming from app store search. There's no secret sauce to this: you just have to use trial and error (and carefully find a way to measure your search rankings) - there are a variety of tools to help you with keeping track of search rankings.
We have share functionality in the app, but its not until the end along with the credits. We've actually already had a complaint that it's too accessible for kids that are using their parents iPad, iPhone etc.
I should also mention that the app is available on both iOS and Android marketplaces. So far we've gotten NO traction in the Android marketplace, so thats an even bigger mystery.