This study presents the development and experimental verification of a mathematical model for the dry fractionation of wheat flour in a pneumatic screw classifier. The model describes the distribution of axial, radial, and tangential airflow components and accounts for the effects of the adjustable aperture opening degree (φ) and material loading coefficient on particle transport and separation. Particle motion was analyzed based on the balance among aerodynamic drag, gravitational, and centrifugal forces, together with particle residence-time and radial-migration conditions. Engineering calculations were performed for a classifier throughput of 150 kg/h, corresponding to a material mass flow rate of 0.0417 kg/s and a material loading coefficient of approximately μ = 0.029. The theoretically predicted effective separation window was 0.188 ≤ φ ≤ 0.477. Experimental studies were conducted over the aperture-opening range φ = 0.10–0.90, and classifier performance was evaluated using fraction yields, normalized purity indices, enrichment selectivities, overall selectivity, recovery selectivity, and fractionation efficiency. Although the individual performance indicators attained their maximum values at different aperture openings, multi-criteria evaluation identified φ = 0.30–0.40 as the most favorable operating range. Within this interval, the intermediate fraction yield was minimized to 17.19-17.57%, while the normalized protein purity index in the light fraction remained within 93.01-93.99%, the normalized starch purity index in the heavy fraction within 95.83-96.52%, overall selectivity within 3.946-3.959, and fractionation efficiency within 78.49-78.92%. Quantitative comparison between calculated and experimental results demonstrated close agreement for all investigated indicators. The coefficients of determination ranged from 0.998 to 1.000, while the mean absolute percentage error did not exceed 4.56%. The highest relative errors were observed in the light and intermediate fraction yields, whereas the normalized purity and selectivity indices were predicted with errors of no more than 0.14%. The proposed model provides a compact engineering tool for evaluating airflow–particle interactions, selecting favorable operating conditions, and optimizing pneumatic screw classifiers to produce protein- and starch-enriched wheat flour fractions.