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We explore the potential of the kinetic Sunyaev-Zel'dovich (kSZ) effect as the cornerstone of a future observational probe for halo spin bias, the secondary dependence of halo clustering on halo spin at fixed halo mass. Using the IllustrisTNG magneto-hydrodynamical cosmological simulation, we measure both the kSZ and the thermal SZ (tSZ) effects produced by the baryonic content of more than 50,000 haloes within the halo mass range $11 < \log_{10} ({\rm M_{vir}}/ h^{-1} {\rm M_{\odot}}) \lesssim 14.5$. First, we confirm that the magnitude of both effects depends strongly on the total gas and virial mass of the haloes, and that the integrated kSZ signal displays a significant correlation with the angular momentum of the intra-halo gas, particularly for massive haloes. Second, we show that both the integrated kSZ signal and the ratio of the integrated kSZ and tSZ signals trace total halo spin, even though significant scatter exists. Finally, we demonstrate that, in the absence of observational and instrumental uncertainties, these SZ-related statistics can be used to recover most of the underlying IllustrisTNG halo spin bias signal. Our analysis represents the first attempt to develop a future observational probe for halo spin bias, bringing forward alternative routes for measuring the secondary bias effects.