The magnification effect of gravitational lensing is a powerful probe of the distribution of matter in the universe, yet it is frequently overlooked due to the fact that its signal-to-noise ratio is smaller than that of lensing shear. Because its systematic errors are quite different from those of shear, magnification is nevertheless an important approach with which to study the distribution of large-scale structure. We present lensing mass profiles of spectroscopic luminous red galaxies (LRGs) and galaxy clusters determined through measurements of the weak lensing magnification of photometric LRGs in their background. We measure the change in detected galaxy counts as well as the increased average galaxy flux behind the lenses. In addition, we examine the average change in source colour due to extinction by dust in the lenses. By simultaneously fitting these three probes we constrain the mass profiles and dust-to-mass ratios of the lenses in six bins of lens richness. For each richness bin we fit a Navarro-Frenk-White halo mass, brightest cluster galaxy mass, second halo term, and dust-to-mass ratio. The resulting mass-richness relation is consistent with previous analyses of the catalogues, and limits on the dust-to-mass ratio in the lenses are in agreement with expectations. We explore the effects of including the (low signal-to-noise ratio) flux magnification and reddening measurements in the analysis compared to using only the counts magnification data; the additional probes significantly improve the agreement between our measured mass-richness relation and previous results. © 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.