Based on the comprehensive analysis of laser kinetics and hydrodynamic processes of alkali vapor laser amplifiers and combined with the thermal effect, saturation amplification effect, amplified spontaneous emission, and high level excitation and ionization, a comparatively ideal physical model is established to simulate the output characteristics of diode-pumped alkali vapor laser amplifiers under flow and heat dissipation conditions. The influence of gas flow velocity on output power is simulated with two different flow modes in longitudinal and transverse directions. The variation trend of the particle number density at high pumping power density is compared and analyzed. Finally, the effect of the power distribution ratio of the amplifier in each stage on the improvement of cascade amplifier output power is simulated. Results show that under the same operating temperature condition, multiple equal-length steam pools and equal distribution of pumping power allow high-level amplifiers to achieve higher magnification than that of low-level amplifiers. Thus, the model contributes to the parametric selection and optimization of the design of alkali vapor laser amplifiers.