Rapid increase of storage and network bandwidth incurs higher CPU consumption in modern data systems. This phenomenon is particularly evident for log-structured merged key-value stores (LSM-KVS), which rely on resource-intensive background operations to flush and compact disk data. While extensive research has been conducted to reduce the CPU overhead of background compaction, less attention has been paid to background flushing, which can also consume a significant amount of valuable CPU cycles and disrupt CPU caches, ultimately impacting overall performance. In this paper, we propose DFlush, a novel solution that uses DPUs to offload background flush operations to reduce its CPU cost. DPUs are an appealing choice for this goal due to their cost-effectiveness, ease of programming, and widespread deployment. However, their complex hardware architecture requires careful design of both the data and control planes. To fully harness the DPU's capabilities, DFlush decomposes a flush job into fine-grained steps, mapped them to DPU hardware units, and accelerates them through pipeline, data, and channel parallelism, ensuring data-plane efficiency. It also introduces an adaptive control plane that dynamically schedules flush jobs from different LSM-KVS instances based on their priority, reducing write stall and tail latency. Our experiments on a real DPU platform with an industrial-grade LSM-KVS show that DFlush delivers higher throughput, significantly lower tail latency, and saves up to dozens of CPU cores per LSM-KVS server while reducing energy consumption.