With the rapid growth of IoT devices, ensuring the security of embedded firmware has become a critical concern. Despite advances in existing vulnerability discovery methods, previous research has been limited to vulnerabilities occurring in binary programs. Although an increasing number of vendors are utilizing Lua scripting language in firmware development, no automated method is currently available to discover vulnerabilities in Lua-based programs. To fill this gap, in this paper, we propose FLuaScan, a novel progressive static analysis approach specifically designed to detect taint-style vulnerabilities in Lua applications in IoT firmware. FLuaScan first heuristically locates the code that handles user input, then divides the code into different segments to conduct a progressive taint analysis. Finally, a graph-based search method is applied to identify vulnerable code that satisfies the conditions of taint propagation. To comprehensively compare FLuaScan with state-of-the-art tool Tscancode, we conducted various experiments on a dataset consisting of 13 real-world firmware samples from different vendors. The results demonstrate the superior performance of FLuaScan in terms of accuracy (increased TP rate from 0% to 42.50%), effectiveness (discovered 21 vulnerabilities, of which 7 are unknown), and practicality (acceptable time overhead and visual output to assist in manual analysis).