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In this paper we consider a human-swarm interaction scenario based on hand gestures. We study how the swarm can incrementally learn hand gestures through the interaction with a human instructor providing training gestures and correction feedback. The main contribution of the paper is a novel incremental machine learning approach that makes the robot swarm learn and recognize the gestures in a distributed and decentralized fashion using binary (i.e., yes/no) feedback. It exploits cooperative information exchange and swarm's intrinsic parallelism and redundancy. We perform extensive tests using real gesture images, showing that good classification accuracies are obtained even with rather few training samples and relatively small swarms. We also show the good scalability of the approach and its relatively low requirements in terms of communication overhead.