I would imagine most people who have taught acting for any length of time—or writing for that matter—will have had someone ask them whether it is actually possible for the subject to be taught, as, surely, people can either do it or they can't. Of course I have my standard explanation for why it isn't as simple as that, but even I was a little sceptical about whether an accent can be learned from a book.
The Compact Guide series from Nick Hern comprises handy-sized books, easy to slip into a bag, on very specific, practical subjects for actors. This one from USA-born voice and dialect coach Rebecca Gausnell has a few exercises that are useful for general voice and accent work, but most of the 184 pages are tailored specifically towards speaking with the accent known as 'General American', which I'm guessing is the US equivalent of British RP. Regional American accents are beyond the scope of the book.
There are some voice recordings to accompany the book which are very useful for illustrating what is being described in words—there is a link to them in Soundcloud in the introduction and each is referenced specifically at some point in the text (I assume they can be played directly from the page in the eBook edition). However the real teaching is done by describing the sounds to be produced and the shape of the mouth and tongue needed to create them—with diagrams—with exercises and texts to practice and improve.
And these exercises are very detailed and specific: the section on the letter 'r' spans 26 pages. However this concentration on the mechanics of producing the sounds is never allowed to distract from the need to incorporate this work into the portrayal of a convincing character who should sound like a native speaker.
This is a book that is very easy to skim through—as I did, although I found myself pulling odd faces at a few points—but to get the most out of it, you should spend time on all of the exercises, which are clearly described and valuable.
While this could never replace working with a good dialect coach, for someone seeking to expand their voice and accent skills or about to go into rehearsal, when there is never enough time to spend on these details even when a coach is available, it would be a worthwhile investment.
So, just as you can, to some extent, teach acting and writing in a class, it seems that you can learn accents from a book.