One puzzle in understanding how stars form in clusters is the source of mass -- is all of the mass in place before the first stars are born, or is there an extended period when the cluster accretes material which can continuously fuel the star formation process? We use a multi-line spectral survey of the southern filament associated with the Serpens South embedded cluster-forming region in order to determine if mass is accreting from the filament onto the cluster, and whether the accretion rate is significant. Our analysis suggests that material is flowing along the filament's long axis at a rate of ~30Msol/Myr (inferred from the N2H+ velocity gradient along the filament), and radially contracting onto the filament at ~130Msol/Myr (inferred from HNC self-absorption). These accretion rates are sufficient to supply mass to the central cluster at a similar rate to the current star formation rate in the cluster. Filamentary accretion flows may therefore be very important in the ongoing evolution of this cluster.