Data flow testing (DFT) focuses on the flow of data through a program. Despite its higher fault-detection ability over other structural testing techniques, practical DFT remains a significant challenge. This paper tackles this challenge by introducing a hybrid DFT framework: (1) The core of our framework is based on dynamic symbolic execution (DSE), enhanced with a novel guided path search to improve testing performance, and (2) we systematically cast the DFT problem as reach ability checking in software model checking to complement our DSE-based approach, yielding a practical hybrid DFT technique that combines the two approaches' respective strengths. Evaluated on both open source and industrial programs, our DSE-based approach improves DFT performance by 60~80% in terms of testing time compared with state-of-the-art search strategies, while our combined technique further reduces 40% testing time and improves data-flow coverage by 20% by eliminating infeasible test objectives. This combined approach also enables the cross-checking of each component for reliable and robust testing results.