We investigate the dispersion of solutes in active nematic fluids confined to narrow channels based on simulations of nematohydrodynamics. The study focuses on two pre-turbulent regimes: oscillatory flow, with net mass flux, and dancing flow, without net flux. Non-diffusive tracers exhibit markedly different behaviors in oscillatory and dancing flows. By contrast, the hydrodynamic dispersion of solutes driven by active flows, both in the oscillatory and dancing flows, are similar and can be described by an extension of the Taylor-Aris law. This study contributes to our understanding of micromixing in active flows both in nature and in applications.