We revisit the paradigm of the dependence of jet power on black hole (BH) spin in accreting BH systems. In a previous paper, we showed that the luminosity of compact jets continuously launched due to accretion on to BHs in X-ray binaries (analogous to those that dominate the kinetic feedback from active galactic nuclei) does not appear to correlate with reported BH spin measurements. It is therefore unclear whether extraction of the BH spin energy is the main driver powering compact jets from accreting BHs. Occasionally, BH X-ray binaries produce discrete, transient (ballistic) jets for a brief time over accretion state changes. Here, we quantify the dependence of the power of these transient jets (adopting two methods to infer the jet power) on BH spin, making use of all the available data in the current literature, which include 12 BHs with both measured spin parameters and radio flares over the state transition. In several sources, regular, well-sampled radio monitoring has shown that the peak radio flux differs dramatically depending on the outburst (up to a factor of 1000), whereas the total power required to energize the flare may only differ by a factor of ≲4 between outbursts. The peak flux is determined by the total energy in the flare and the time over which it is radiated (which can vary considerably between outbursts). Using a Bayesian fitting routine, we rule out a statistically significant positive correlation between transient jet power measured using these methods and current estimates of BH spin. Even when selecting sub-samples of the data that disregard some methods of BH spin measurement or jet power measurement, no correlation is found in all cases.