An x-ray spectrometer devoted to dynamical studies of transient systems using the x-ray absorption fine spectroscopy technique is presented in this article. Using an ultrafast laser-induced x-ray source, this optical device based on a set of two potassium acid phthalate conical crystals allows the extraction of x-ray absorption near-edge spectroscopy structures following the Al absorption K edge. The proposed experimental protocol leads to a measurement of the absorption spectra free from any crystal reflectivity defaults and shot-to-shot x-ray spectral fluctuation. According to the detailed analysis of the experimental results, a spectral resolution of 0.7 eV rms and relative fluctuation lower than 1% rms are achieved, demonstrated to be limited by the statistics of photon counting on the x-ray detector.