This article proposes REACT, a regular expression matching accelerator, which can be embedded in a modern Solid-State Drive (SSD) and a novel data access scheduling algorithm for high matching throughput. Specifically, REACT, including our data access scheduling algorithm, increases the utilization of SSD and the degree of internal memory parallelism for pattern matching processes. While the low-level flash exhibits long latency, modern SSDs in practice achieve high I/O performance by utilizing the massive internal parallelism at the system-level. However, exploiting the parallelism is limited for pattern matching since the sub-blocks, which constitute an input data and can be placed in multiple flash pages, should be tested in a sequence to process the input correctly. This limitation can induce low utilization of the accelerator. To address this challenge, the proposed REACT simultaneously processes multiple input streams with a parallel processing architecture to maximize matching throughput by hiding the long and irregular latency. The scheduling algorithm finds a data stream which requires a sub-block in closest time and prioritizes the access request to reduce the data stall of REACT. REACT achieves maximum 22.6 percent of matching throughput improvement on a 16-channel high-performance SSD compared to the accelerator without the proposed scheduling algorithm.