Turbulent mixing processes and species transport govern many important properties like stability and pollutant formation of reactive systems. We propose spectrally resolved absorption tomography as a viable tool to quantitatively assess species transport by imaging tracer pulses at high time resolution. Measurements on a gas-assisted solid-fuel combustor operating in air and oxy-fuel atmospheres are presented. The measurements are conducted using a scanning tomographic imaging system that has previously been validated for gas temperature measurements. As the scanning system itself is not able to achieve the necessary time resolution, a phase-locked tomographic scheme is applied, i.e. each measurement beam is acquired separately for several tracer pulses and phase-averaged. Hence, the full 5 kHz time resolution of the underlying tunable diode laser spectroscopy system can be utilized, granting insight into species transport in the recirculation zones as well as the flame brush. Despite a possible influence of the tracer injections on the inner recirculation zone, it is shown that qualitative differences between methane combustion and gas-assisted solid-fuel operating conditions can be detected, and influences of devolatilization as well as volatile combustion become visible.