Controlled manipulation of neutron spin is a critical tool for many neutron scattering techniques. We have constructed current-sheet, neutron spin flippers for use in Spin Echo Scattering Angle Measurement (SESAME) that comprise pairs of open-faced solenoids which introduce an abrupt field reversal at a shared boundary. The magnetic fields generated by the coils have been mapped and compared with both an analytical approximation and a numerical boundary integral calculation. The agreement is generally good, allowing the former method to be used for rapid calculations of the Larmor phase acquired by a neutron passing through the flipper. The evolution of the neutron spin through the current sheets inside the flipper is calculated for various geometries of the current-carrying conductors, including different wire shapes, arrangements, and common imperfections. The flipping efficiency is found to be sensitive to gaps between wires and between current sheets. SESAME requires flippers with high fields and flipping planes inclined to the neutron beam. To avoid substantial neutron depolarization, such flippers require an interdigitated arrangement of wires.