We report an alternative random laser (RL) architecture based on a flexible and ZnO-enriched cellulose acetate (CA) fiber matrix prepared by electrospinning. The electrospun fibers, mechanically reinforced by polyethylene oxide and impregnated with zinc oxide powder, were applied as an adsorbent surface to incorporate plasmonic centers (silver nanoprisms). The resulting structures - prepared in the absence (CA-ZnO) and in the presence of silver nanoparticles (CA-ZnO-Ag) - were developed to support light excitation, guiding and scattering prototypes of a RL. Both materials were excited by a pulsed (5 Hz, 5 ns) source at 355 nm and their fluorescence emission monitored at 387 nm. The results suggest that the addition of silver nanoprisms to the ZnO- enriched fiber matrix allows large improvement of the RL performance due to the plasmon resonance of the silver nanoprisms, with ~80% reduction in threshold energy. Besides the intensity and spectral analysis, the RL characterization included its spectral and intensity angular dependences. Bending the flexible RL did not affect the spectral characteristics of the device. No degradation was observed in the random laser emission for more than 10,000 shots of the pump laser.