Solar chimneys are passive ventilation systems that leverage solar energy to supplement or replace mechanical ventilation. Here we present a novel flow network analysis method for solar chimneys in high-rise buildings and use this method to develop insights into the design of these systems in high-rise multi-unit residential buildings (MURBs). The proposed method differs from others as it relies on a flow network that is less computationally intensive than computational fluid dynamics methods, but it can consider more complex system layouts than existing flow network methods, allowing for characterization of these systems in high-rise buildings. The method was validated by comparing results to other studies in the literature, showing that it can match the flow rates reported for single-floor systems within a 5% error, and qualitatively match the trends from studies of multi-floor systems. We use a case study to demonstrate how the model can be used to analyze the performance of a solar chimney in a high-rise MURB. The results indicate that the air flow rate to each floor induced by the solar chimney is proportional to collector width and solar flux, and inversely proportional to the inlet temperature and the number of floors. The method detailed in this study can be used by practitioners and researchers to develop simulation programs, and the case study results can be used to improve solar chimney design in high-rise MURBs.