The nanocomposite Cu–Cr powder was consolidated by flash spark plasma sintering (FSPS), which involves applying an extremely rapid change in the electrical power passing through the bulk of the sample. It was demonstrated that an essentially fully dense material could be obtained in 15 s. Such short-term treatment typically preserves the nanostructured features of the material. However, investigation revealed a nonuniformity in the microstructure of the alloys obtained under such extreme conditions. To better understand the observed effects, the FSPS process was simulated. It was observed that a rapid change in the applied electrical power resulted in nonuniform distributions of current density and temperature along the body of the consolidated material. Specifically, the current density was higher on the periphery of the sample, and the temperature was higher in the middle. These findings explain the observed structural transformation during FSPS and suggest an optimization strategy to avoid microstructural nonuniformity.