We apply ultrafast pure-rotational coherent anti-Stokes Raman scattering (CARS) for temperature and relative oxygen concentration measurements in the plume emanating from a burning, aluminized ammonium-perchlorate propellant strand. Combustion of these metal-based propellants is a particularly hostile environment for laser-based diagnostics, with intense background luminosity and scattering from hot metal particles as large as several hundred micrometers in diameter. CARS spectra that were previously obtained using nanosecond pulsed lasers in an aluminum-particle-seeded flame are examined and are determined to be severely impacted by nonresonant background, presumably as a result of the plasma formed by particulate-enhanced laser-induced breakdown. Introduction of femtosecond/picosecond (fs/ps) laser pulses improves CARS detection by providing time-gated elimination of strong nonresonant background interference. Single-laser-shot fs/ps CARS spectra were acquired from the burning propellant plume, with picosecond probe-pulse delays of 0 and 16 ps from the femtosecond pump and Stokes pulses. At zero delay, nonresonant background overwhelms the Raman-resonant spectroscopic features. Time-delayed probing results in the acquisition of background-free spectra that were successfully fit for temperature and relative oxygen content. Temperature probability densities and temperature/oxygen correlations were constructed from ensembles of several thousand single-laser-shot measurements with the CARS measurement volume positioned within 3 mm or less of the burning propellant surface. The results show that ultrafast CARS is a potentially enabling technology for probing harsh, particle-laden flame environments.