Static analysis is known to yield numerous false alarms when used in bug finding, especially for complex vulnerabilities in large code bases like the Linux kernel. One important class of such complex vulnerabilities is what we call "high-order taint style vulnerability", where the taint flow from the user input to the vulnerable site crosses the boundary of a single entry function invocation (i.e., syscall). Due to the large scope and high precision requirement, few have attempted to solve the problem. In this paper, we present SUTURE, a highly precise and scalable static analysis tool capable of discovering high-order vulnerabilities in OS kernels. SUTURE employs a novel summary-based high-order taint flow construction approach to efficiently enumerate the cross-entry taint flows, while incorporating multiple innovative enhancements on analysis precision that are unseen in existing tools, resulting in a highly precise inter-procedural flow-, context-, field-, index-, and opportunistically path-sensitive static taint analysis. We apply SUTURE to discover high-order taint vulnerabilities in multiple Android kernels from mainstream vendors (e.g., Google, Samsung, Huawei), the results show that SUTURE can both confirm known high-order vulnerabilities and uncover new ones. So far, SUTURE generates 79 true positive warning groups, of which 19 have been confirmed by the vendors, including a high severity vulnerability rated by Google. SUTURE also achieves a reasonable false positive rate (51.23%) perceived by users of our tool.