Non-intrusive flow measurement methods are increasingly required in pipeline systems to eliminate pressure losses, prevent contamination, and avoid structural modifications. Flow-induced vibration (FIV) offers a promising alternative; however, its applicability to standard industrial carbon-steel pipelines and its integration with data-driven modeling remain limited. This study experimentally investigates FIV-based flow estimation in 1-inch PVC and carbon-steel pipes conveying water under controlled conditions using regression, and machine learning models, while examining the influence of pipe material and vibration-response characteristics on flow-rate prediction performance. Vibration responses were measured using a tri-axial accelerometer and analyzed to identify flow-sensitive frequency bands. Regression and machine-learning models were developed to relate vibration characteristics to flow rate. The results demonstrate a predominantly monotonic relationship between band-averaged vibration amplitude and flow rate, with material-dependent sensitivity observed between PVC and carbon-steel pipes. Data-driven models improved prediction performance and robustness on the dynamic behavior of flow-induced vibrations, The findings demonstrate the potential of combining FIV analysis with intelligent modeling as a non-intrusive approach for flow measurement in industrial pipelines. Neural time-series modeling was used for training purpose only. Open-loop training provides a stable and efficient way for the network to learn the underlying dynamic relationship between inputs and outputs. A meaningful assessment of the model's predictive capability requires closed-loop testing, where the network relies on its own previous predictions. This was not conducted in the present study.