Trusted execution environments (TEE) such as Intel's Software Guard Extension (SGX) have been widely studied to boost security and privacy protection for the computation of sensitive data such as human genomics. However, a performance hurdle is often generated by SGX, especially from the small enclave memory. In this paper, we propose a new Hybrid Secured Flow framework (called "HySec-Flow") for large-scale genomic data analysis using SGX platforms. Here, the data-intensive computing tasks can be partitioned into independent subtasks to be deployed into distinct secured and non-secured containers, therefore allowing for parallel execution while alleviating the limited size of Page Cache (EPC) memory in each enclave. We illustrate our contributions using a workflow supporting indexing, alignment, dispatching, and merging the execution of SGX- enabled containers. We provide details regarding the architecture of the trusted and untrusted components and the underlying Scorn and Graphene support as generic shielding execution frameworks to port legacy code. We thoroughly evaluate the performance of our privacy-preserving reads mapping algorithm using real human genome sequencing data. The results demonstrate that the performance is enhanced by partitioning the time-consuming genomic computation into subtasks compared to the conventional execution of the data-intensive reads mapping algorithm in an enclave. The proposed HySec-Flow framework is made available as an open-source and adapted to the data-parallel computation of other large-scale genomic tasks requiring security and scalable computational resources.