Energy efficiency and computing flexibility are some of the primary design constraints of heterogeneous computing. In this paper, we present FlashAbacus, a data-processing accelerator that self-governs heterogeneous kernel executions and data storage accesses by integrating many flash modules in lightweight multiprocessors. The proposed accelerator can simultaneously process data from different applications with diverse types of operational functions, and it allows multiple kernels to directly access flash without the assistance of a host-level file system or an I/O runtime library. We prototype FlashAbacus on a multicore-based PCIe platform that connects to FPGA-based flash controllers with a 20 nm node process. The evaluation results show that FlashAbacus can improve the bandwidth of data processing by 127%, while reducing energy consumption by 78.4%, as compared to a conventional method of heterogeneous computing.