Agree with Nanren888. Totally normal in the context of proofreading text and in the context of book reviews. Oxford-Hachette Dictionary: Read meaning #3 (create an impression) the document reads well/badly

Hmmm.. it's not very common, but I understand it. Usually you read something to someone and say 'Does this sound ok?' I think on this case you want the other person to read it, so it means 'does this seem ok when you read it?' :)

Not quite slang but definitely colloquial. 'read' here could be used to ask if whatever is written sounds natural, or, if the person has to read it out loud, does the sentence 'read' ok might mean is it easy to say - especially true if the sentence is long or contains dense noun clauses.

Absolutely normal for anyone who checks writing. Not slang at all. . I've penned this paragraph for cover Margo leaving. Can you check that it reads ok and does not step on any toes? . I was having trouble with the introduction. Can you have a look and tell me if you thinks it reads ok? . Let me know whether you think this answer reads ok. . From the range of answers, I'd guess the frequency of use is regionally-dependent. . I have no sense of "out loud". Simply whether it makes sense, is understandable, clear, not <insert any bad adjective from context>. In short, "ok". . :) The introduction while more than a little obstruse without needing to be was in short a waste of time and effort, with few redeeming features excepting the illustrative aspect that was so torturously built into it and so obviously contrived. <-- Does not read ok.