The $\Lambda$ cold dark matter ($\Lambda$CDM) standard cosmological model isin severe tension with several cosmological observations. Foremost is theHubble tension, which exceeds $5\sigma$ confidence. Galaxy number counts showthe Keenan-Barger-Cowie (KBC) supervoid, a significant underdensity out to300~Mpc that cannot be reconciled with $\Lambda$CDM cosmology. Haslbauer et al.previously showed that a high local Hubble constant arises naturally due togravitationally driven outflows from the observed KBC supervoid. The mainprediction of this model is that peculiar velocities are typically much largerthan expected in the $\Lambda$CDM framework. This agrees with the recentdiscovery by Watkins et al. that galaxies in the CosmicFlows-4 catalogue havesignificantly faster bulk flows than expected in the $\Lambda$CDM model onscales of $100-250 \, h^{-1}$~Mpc. The rising bulk flow curve is unexpected instandard cosmology, causing $4.8\sigma$ tension at $200 \, h^{-1}$~Mpc. In thiswork, we determine what the semi-analytic void model of Haslbauer et al.predicts for the bulk flows on these scales. We find qualitative agreement withthe observations, especially if our vantage point is chosen to match theobserved bulk flow on a scale of $50 \, h^{-1}$~Mpc. This represents a highlynon-trivial success of a previously published model that was not constrained bybulk flow measurements, but which was shown to solve the Hubble tension andexplain the KBC void consistently with the peculiar velocity of the LocalGroup. Our results suggest that several cosmological tensions can besimultaneously resolved if structure grows more efficiently than in the$\Lambda$CDM paradigm on scales of tens to hundreds of Mpc.