In-storage processing (ISP) efficiently examines large datasets but faces performance and security challenges. We introduce DockerSSD, a flexible ISP model that runs various applications near flash without modification. It employs lightweight OS-level virtualization in modern SSDs for faster ISP and better storage intelligence with a high flexiblity. DockerSSD reuses existing Docker container images for real-time data processing without altering the storage interface or runtime. Our design includes a new communication method and virtual firmware, alongside automated container-related network and I/O handling hardware. DockerSSD achieves a 2× speed improvement and reduces system-level power by 35.7%, on average.