Weak magnetic fields produced by the combustion of pure metal and metal/metal-oxide powders in flowing oxygen were measured by High-Tc Superconducting Quantum Interference Devices (SQUIDs). Two qualitatively different types of magnetic signals were observed for various reactions. The combustion of Nb, Cr, and Co generates a slowly oscillating field, while the combustion of Zr, Hf, Mn, Ti, Mg, and Fe generates a slowly oscillating field on which rapid oscillations are superimposed. The magnetic power spectra for these reactions scales as a power-law up to 100 Hz with an exponent between 0.64 and 0.96. This suggests that the magnetic field oscillations are generated by stochastic current fluctuations over a wide range of time scales. This may result from fluctuations in either the instantaneous shape and/or the velocity of the reaction zone. A simple electromagnetic model is used to predict the qualitative features observed in our experiments.