Have you tried VoiceOver? On iOS, turn it on by triple-clicking the Home button, then two-fingered swipe downward to start speaking continuously until the end of the book.
No kidding. It's intended for the blind, and using it this way is more like a well-supported hack than a feature.
However, Apple and Amazon's hands may be tied by contracts. Amazon tried to introduce general-purpose text-to-speech in the Kindle 2, but soon retracted it when rights-holders asserted that such a feature required paying a separate audiobook royalty.
Roy Blount Jr., in his role as the president of the Authors Guild, set forth that position in an NYT editorial titled "The Kindle Swindle". Noting the public opposition of the National Federation of the Blind, he specifically exempted assistive technologies.
Perhaps the triple-click shortcut is turned off for some reason, though a quick search indicated that it was on by default in iOS 6 and 7. Normally double-click is enough to show all running apps.
You could check in Settings -> General -> Accessibility -> Accessibility Shortcut.
You're right, it was turned off. I do need to select text first. This makes it not very usefull for iBook ebooks. You' like continues reading. Oh well, audio books for now.
If you need to select text, something still isn't working properly. You should be able to drag two fingers down from the top of the screen, and it will read and turn pages for you until the end of the book.
