Performance of solar absorption cooling systems (SACS) is the focus of contemporary studies for decreasing the electrical energy consumption of buildings as the conventional cooling system of buildings is the main consumer of electrical energy during the summer season in hot–humid climates. In this study, the performance analysis of SACS by manipulating different flow schemes to the heat transfer fluid between different components of the system was performed. TRNSYS model of SACS in an education building located at the city of Peshawar (34.00 N, 71.54 E), Pakistan to encounter the peak cooling load of 108 kW (during operating hours of the building i.e., 09 a.m. to 05 p.m.) is developed and all possible flow schemes of heat transfer fluid between the system’s components were compared. In Scheme-1 (S-1), a conventional flow pattern is used in which the hot water exiting from the chiller unit flows directly toward the stratified thermal storage unit. In Scheme-2 (S-2), the modified flow pattern of hot water exiting from the chiller unit will divert towards the auxiliary unit, if its temperature exceeds the temperature at the hot side outlet of the tank. Another modified flow pattern is Scheme-3 (S-3) in which the hot water leaving the chiller to keep diverting towards the auxiliary unit unless the outlet temperature from the hotter side of the tank would reach the minimum driving temperature (109 °C) of the chiller’s operation. Simulations in TRNSYS evaluates the SACS’s performance of all the schemes (conventional and modified) for the whole summer season and for each month. In general, S-3 with evacuated tube solar collector results in better primary energy saving with the smallest collector area per kilowatt for achieving 50% primary energy saving for the whole summer season.