Related to the issue of chiasmus in the Book of Mormon is the Hebrew tool called inclusio, in which a phrase at the beginning of a passage is mirrored at the end to mark a section. Interesting insight into a sophisticated case (or 3 related cases) of inclusio in the Book of Mormon is treated by Reynolds in a peer-reviewed publication: Noel B. Reynolds (2015). The Gospel according to Mormon. Scottish Journal of Theology, 68, pp 218-234. doi:10.1017/S003693061500006X, available for download at http://scholarsarchive.byu.edu/facpub/1479/.
Reynolds' work reveals some consistent elements in the text regarding the Book of Mormon's concept of the core doctrine of the Gospel, and the way its authors use inclusio to emphasize it. It's one of many interesting subtleties in the composition of the text.
Speaking of chiasmus, one of my favorite works related to the Book of Mormon in a non-LDS publication is John Welch's chapter on chiasmus in the Book of Mormon, included in the ground-breaking book on chiasmus that he edited, in collaboration with some significant scholars and published through a noteworthy publishing house. The reference is: John W. Welch, editor, Chiasmus in Antiquity: Structures, Analyses, Exegesis (Hildesheim, Germany: Gerstenberg Verlag, 1981). This scholarly work in a non-LDS press with non-LDS authors (apart from John) includes a forward from Dr. David Noel Freedman.
I recommend reading David Noel Freedman's preface to the scholarly book, Chiasmus in Antiquity, edited by John Welch. The full text of that intriguing book is available free online at the Maxwell Institute. Here is part of what Dr. Freedman has to say:
The more extended uses of chiasm raise further questions. As with much of literature, especially poetry, ambiguity and obscurity are inherent in the form and content: chiasm only adds to the uncertainty and mystery. Scholars now recognize chiasms beyond the simple type described above, chiasms which involve passages of verse or prose ranging in length from a few sentences to hundreds of thousands of words. This more complex form of chiasm is not merely grammatical but structural or intentional; it systematically serves to concentrate the reader's or hearer's interest on the central expression. The number of such chiastic constructions which satisfy both sets of criteria: inversion and balance on the one hand, and climactic centrality on the other, is substantially less than the simpler mechanical variety. But wherever they are present, these structures may add novel perspectives and unexpected dimension to the texts in which they appear.Dr. Freedman has been called one of the world's foremost scholars on the Bible. You can also read about him on Wikipedia. He passed away in 2008.
There is yet a further extension of the term chiasm. Even more difficult and controversial issues arise when chiasm is defined in terms of thought and theme, rather than the more visible words and patterns. Inevitably a large subjective element enters into these discussions, and the presence or absence of chiasm on this level can become almost a voter's choice.
Scholars, therefore, may range between separated areas of research in their approach to chiasm. On the one extreme, the phenomenon itself can be described or defined rigorously, so that it is verifiable and often self-evident; while in this sense it is part of a deliberate pattern of composition, it nevertheless leaves the wider world of symbolism and significance to others. At the other end of the spectrum, definitions and limits are hard to determine, and speculation is rife; but large issues of meaning and intention can be raised, and important questions about the nature and significance of extended literary pieces are considered. The study of these great chiasms has enormous implications for analysis and interpretation, but the wider the scope and the more extended the reach, the less certain the results necessarily become. In the end, neither approach will escape if carried to extremes.
Only a book with many varieties of presentation can display the present state of chiastic studies. While a great deal of important work has been done across the many domains of ancient literature, the study of ancient literary techniques is still in ferment and flux. A common fund of axioms and assumptions and a single sure-handed methodology are yet to be established. The present volume reflects accurately both the ferment and the progress which is being made on a variety of fronts, and is all the more to be welcomed for bringing together the results of research in different literatures of antiquity. The editor is to be commended for his catholicity and courage, and for his own original contributions in several domains including a unique treatment of the Book of Mormon. His introduction to the whole work is indispensable. [emphasis added]
--David Noel Freedman
Welch's book is cited by Roland Meynet in Rhetorical Analysis: An Introduction to Biblical Rhetoric. Journal for the Study of the Old Testament Supplement Series 256 (Sheffield, England: Sheffield Academic Press, 1998), 392 pp. I don't have access to it at the moment, but according to Noel Reynolds, "Meynet credits BYU’s own John W. Welch, whose 1981 book re-ignited chiasmus studies and helpfully provided the world of biblical scholars with the first complete bibliography of chiasmus publications, enabling contemporary scholars to get a grasp on the extent and quality of the work that had already been done."