There is no federal common-law accountant–client privilege. Couch v. United States, 409 U.S. 322 (1973). Some, but not all, states recognize an accountant–client privilege, but the privilege’s scope and application vary.
In diversity-jurisdiction actions, federal courts apply the privilege law as dictated by the conflict-of-laws rules of the 
forum state. For an example of how these issues become tangled, see my post discussing a federal court applying Georgia’s accountant–client privilege to a Texas party and his North Carolina-based accountant.
Matters become even trickier when the Judicial Panel on Multi-District Litigation consolidates several federal-court cases into a single MDL court. Convoluted choice-of-law issues arise, particularly regarding application of state-created evidentiary privileges.
Kelly J. Balkin identifies and discusses these complicated issues in her excellent law-review article, The Accountant–Client Privilege in Multidistrict Litigation: An Efficient Federal Common Law Solution, 69 U. Miami L. Rev. 833 (2015). In this article, available here , Ms. Balkin summarizes in a straight-forward manner the state and federal conflict-of-laws issues with respect to evidentiary privileges, and then proposes that MDL courts apply a blanket accountant–client privilege in MDL proceedings where at least one party had relied on the privilege in its accountant dealings.
This article is worth reading for understanding the federal and state conflict-of-laws rules in applying evidentiary privileges in general, as well as for those litigants confronting trouble applying a state-law privilege when a MDL court assumes control of multiple, related actions. And you will also find helpful another article, cited by Ms. Balkin, titled The Application of Conflict of Laws to Evidentiary Privileges, and available here.
My thanks to Kelly Balkin and The University of Miami Law Review for permission to re-publish this first-rate article in this post.