High-speed imaging is central to the experimental investigation of fast phenomena, like flapping flags. Event-based cameras use new types of sensors that address typical challenges such as low illumination conditions, large data transfer, and the trade-off between increasing repetition rate and measurement duration more efficiently and at reduced costs compared to classical frame-based fast cameras. Event-based cameras output unstructured data that frame-based algorithms can not process. This paper proposes a general method to reconstruct the motion of a slender object similar to the centreline of a flapping flag from raw streams of event data. The method takes advantage of continuous illumination, and the reconstruction update rate is set after and independent of the data collection. Our algorithm relies on a coarse chain-like structure that encodes the current state of the line and is updated by the occurrence of new events. The algorithm is applied to synthetic data, generated from known motions, to demonstrate that the method is accurate up to one percent of error for tip-based, shape-based, and modal decomposition metrics. Degradation of the reconstruction accuracy due to simulated defects only occurs when the severity of the defects is more than two orders of magnitude larger than what we typically encounter in experiments. The algorithm is then applied to experimental data of flapping flags, and we obtain relative errors below one percent when comparing the results with the data from laser distance sensors. The reconstruction of line deformation from event-based data is accurate and robust, and unlocks the ability to perform autonomous measurements in experimental mechanics.