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Proper indoor ventilation through buildings' heating, ventilation, and air conditioning (HVAC) systems has become an increasing public health concern that significantly impacts individuals' health and safety at home, work, and school. While much work has progressed in providing energy-efficient and user comfort for HVAC systems through IoT devices and mobile-sensing approaches, ventilation is an aspect that has received lesser attention despite its importance. With a motivation to monitor airflow from building ventilation systems through commodity sensing devices, we present FlowSense, a machine learning-based algorithm to predict airflow rate from sensed audio data in indoor spaces. Our ML technique can predict the state of an air vent-whether it is on or off-as well as the rate of air flowing through active vents. By exploiting a low-pass filter to obtain low-frequency audio signals, we put together a privacy-preserving pipeline that leverages a silence detection algorithm to only sense for sounds of air from HVAC air vent when no human speech is detected. We also propose the Minimum Persistent Sensing (MPS) as a post-processing algorithm to reduce interference from ambient noise, including ongoing human conversation, office machines, and traffic noises. Together, these techniques ensure user privacy and improve the robustness of FlowSense. We validate our approach yielding over 90% accuracy in predicting vent status and 0.96 MSE in predicting airflow rate when the device is placed within 2.25 meters away from an air vent. Additionally, we demonstrate how our approach as a mobile audio-sensing platform is robust to smartphone models, distance, and orientation. Finally, we evaluate FlowSense privacy-preserving pipeline through a user study and a Google Speech Recognition service, confirming that the audio signals we used as input data are inaudible and inconstructible.