Esri provides the following document entitled, ArcGIS Workflow Manager Database Design Doc.pdf.
This document is installed with ArcGIS Workflow Manager Desktop, and is located in the Help folder. For example:
C:\Program Files (x86)\WMX\Desktop10.1\Help\ ArcGIS Workflow Manager Database Design Doc.pdf
Within this .pdf document, a summary of the ArcGIS Workflow Manager user privileges can be found in Appendix A. The guidelines shown for the WMX user are based on that user having all WMX application privileges.
WMX Administrators must have select, update, insert, and delete privileges on all WMX system tables.