We present a high-flux source of cold strontium atoms based on a two-dimensional magneto-optical trap (2D MOT) and a Zeeman slower. We use the source to load a 3D MOT in a separate science chamber, observing a loading rate of 4×1010 atoms/s—to our knowledge, the highest reported loading flux for strontium. To characterize the vacuum pressure in the science chamber, we load the atoms into a magnetic trap and measure a lifetime of between 8 and 24 s, depending on the oven temperature. Finally, we characterize the atom flux and velocity distributions from the oven and from the 2D MOT source, finding reasonable agreement with models in the free molecular flow regime. Our results show that it is possible to readily produce a cold strontium flux at comparable levels to those of alkali species, at oven temperatures compatible with long-term operation, and at vacuum pressures suitable for state-of-the-art quantum experiments. We make our design available at no cost to benefit researchers in the quantum community.