I've published both of my books so far (one of them a collection probably somewhat similar to yours) through CreateSpace, and they've been great for me. They don't publish as an app, obviously, but an ebook version gets listed on the kindle store, which is pretty sweet. For an entire app you'd probably have to do it from scratch, which I have no experience with whatsoever. Personally, I don't see the appeal to doing it that way, but it's up to you.
Thanks for the reply. I want to do an App because then it opens it up to people who don't have eBook readers and spend a lot of time on their phones. Is there a way to offer eBooks through the App Store?
You could look into Google Play Books. It's something I haven't done because it's not offered in my country yet (though I really should give it a shot anyway). I don't think the App Store has an equivalent, though, but I'm not sure about that.