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Computational vision-based flame detection has drawn significant attention in the past decade with camera surveillance systems becoming ubiquitous. Whereas many discriminating features, such as color, shape, texture, etc., have been employed in the literature, this paper proposes a set of motion features based on motion estimators. The key idea consists of exploiting the difference between the turbulent, fast, fire motion, and the structured, rigid motion of other objects. Since classical optical flow methods do not model the characteristics of fire motion (e.g., non-smoothness of motion, non-constancy of intensity), two optical flow methods are specifically designed for the fire detection task: optimal mass transport models fire with dynamic texture, while a data-driven optical flow scheme models saturated flames. Then, characteristic features related to the flow magnitudes and directions are computed from the flow fields to discriminate between fire and non-fire motion. The proposed features are tested on a large video database to demonstrate their practical usefulness. Moreover, a novel evaluation method is proposed by fire simulations that allow for a controlled environment to analyze parameter influences, such as flame saturation, spatial resolution, frame rate, and random noise.