Melt flow is often quoted as the reason for a discrepancy between experiment and theory on dendritic growth kinetics at low undercoolings. But this flow effect is not justified for glass-fluxed melts where the flow field is weaker. In the present work, we modeled the thermal history, flow pattern and dendritic structure of a glass-fluxed nickel sample by magnetohydrodynamics calculations. First, the temperature distribution and flow structure in the molten and undercooled melt were simulated by reproducing the observed thermal history of the sample prior to solidification. Then the dendritic structure and surface temperature of the recalescing sample were simulated. These simulations revealed a large thermal gradient crossing the sample, which led to an underestimation of the real undercooling for dendritic growth in the bulk volume of the sample. By accounting for this underestimation, we recalculated the dendritic tip velocities in the glass-fluxed nickel melt using a theory of three-dimensional dendritic growth with convection and concluded an improved agreement between experiment and theory.