Transient coaxial helicity injection (CHI), a nonsolenoidal method to initiate an inductive-like tokamak plasma discharge, has been demonstrated on the small helicity injected torus (HIT-II), the National Spherical Torus Experiment (NSTX), and the QUEST experiment in Japan. Implementation of transient CHI is underway on the Pegasus-III spherical tokamak (ST) at the University of Wisconsin–Madison. These STs used toroidal ceramic insulators to electrically separate their inner and outer vessel components. Recently, transient CHI was demonstrated on QUEST, an ST that features a single floating-biased electrode configuration. We prepare to demonstrate transient CHI on Pegasus-III, an ST featuring double floating-biased electrodes. This type of electrode configuration, by inhibiting spurious electrical discharges, may be optimal for transient CHI. Transient CHI requires a gas injector system tailored to Pegasus-III that can initiate a CHI discharge by delivering a correctly tailored gas puff to the injector region. Though deliberate choices in the system architecture may optimize gas flow for CHI discharge, there are no simple relations for transient gas flow rates through conduits. In a first for transient CHI, we apply computational fluid dynamics (CFD) simulations to model two different conduit configurations for the Pegasus-III gas injection system. Our results suggest that gas flow through an injector appropriate to Pegasus-III can deliver deuterium at a sufficient rate and quantity to induce CHI discharge but also identify improvements to this configuration. These results are in line with simulations of the CHI injector used on NSTX. This suggests that simulations may outperform analytical approximations as a means to estimate flow rates. This will reduce experimental iterations required to demonstrate transient CHI on Pegasus-III. Simulations such as these are essential for the design of gas injection systems for a fusion reactor equipped with transient CHI capability. The fundamental results presented in this study have broader application to other ST devices.