As a novel member of flexible antennas, the pinching antenna (PA) is realized by integrating small dielectric particles on a waveguide, offering unique regulatory capabilities on constructing line-of-sight (LoS) links and enhancing transceiver channels, reducing path loss and signal blockage. Meanwhile, non-orthogonal multiple access (NOMA) has become a potential technology of next-generation communications due to its remarkable advantages in spectrum efficiency and user access capability. The integration of PA and NOMA enables synergistic leveraging of PA's channel regulation capability and NOMA's multi-user multiplexing advantage, forming a complementary technical framework to deliver high-performance communication solutions. However, the use of successive interference cancellation (SIC) introduces significant security risks to power-domain NOMA systems when internal eavesdropping is present. To this end, this paper investigates the physical layer security of a PA-aided NOMA system where a nearby user is considered as an internal eavesdropper. We enhance the security of the NOMA system through optimizing the radiated power of PAs and analyze the secrecy performance by deriving the closed-form expressions for the secrecy outage probability (SOP). Furthermore, we extend the characterization of PA flexibility beyond deployment and scale adjustment to include flexible regulation of PA coupling length. Based on two conventional PA power models, i.e., the equal power model and the proportional power model, we propose a flexible power strategy to achieve secure transmission. The results highlight the potential of the PA-aided NOMA system in mitigating internal eavesdropping risks, and provide an effective strategy for optimizing power allocation and cell range of user activity.