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Reconfigurable intelligent surfaces (RISs) can shape the wireless environment for enhancing the communication performance. In this letter, we propose a cooperative multi-RIS assisted transmission scheme for a millimeter-wave multi-antenna orthogonal frequency division multiplexing system. We first put forward a delay matching based scheme for simultaneously estimating the multipath channels and the transmission delays of distributed RISs, which requires limited training overhead and feedback. Based on this scheme, we obtain a closed-form solution for the RIS phase shift. Then, we derive an analytical expression of the downlink rate, which is proved to increase logarithmically with the square number of RIS reflecting elements. Simulations are conducted to verify these observations.