We demonstrate the highest flux tabletop source of coherent soft X-rays to date, driven by a single-stage 10 mJ Ti:sapphire regenerative amplifier at 1 kHz. We first down-convert the laser to 1.3 µm using a parametric amplifier, before up-converting it to soft X-rays using high harmonic generation in a high-pressure, phase matched, hollow waveguide geometry. The resulting optimally phase matched broadband spectrum extends to 200 eV, with a soft X-ray photon flux of > 10(6) photons/pulse/1% bandwidth at 1 kHz, corresponding to > 10(9) photons/s/1% bandwidth, or approximately a three order-of-magnitude increase compared with past work. Finally, using this broad bandwidth X-ray source, we demonstrate X-ray absorption spectroscopy of multiple elements and transitions in molecules in a single spectrum, with a spectral resolution of 0.25 eV, and with the ability to resolve the near edge fine structure.