Shingi wasn't too surprised by her request for a couple of reasons. Firstly it was rare for monsters to know how to read the common language since humans mainly used it. What surprised him, though, was that Anyuim made the request in the common language, not Draconic.
Before, when she spoke to her, she didn't seem to know how to speak anything but Draconic, but it could be that she was keeping it a secret. Even if she appeared willing to serve him, that didn't mean she wasn't withholding anything from him. Shingi was certain that she hadn't shared all the details of her tale of how they came to be in the Tower, but he had decided to let it go for now.
But even if she knew how to read common, reading the book would be impossible as it wasn't written in the common language of this world. The book was written in English, and even if the way they spoke was pretty much English, its writing was far from being similar to it.