Low-altitude wireless networks (LAWNs) are expected to play a central role in future 6G infrastructures, yet uplink transmissions of uncrewed aerial vehicles (UAVs) remain vulnerable to eavesdropping due to their limited transmit power, constrained antenna resources, and highly exposed air-ground propagation conditions. To address this fundamental bottleneck, we propose a flexible-duplex cell-free (CF) architecture in which each distributed access point (AP) can dynamically operate either as a receive AP for UAV uplink collection or as a transmit AP that generates cooperative artificial noise (AN) for secrecy enhancement. Such AP-level duplex flexibility introduces an additional spatial degree of freedom that enables distributed and adaptive protection against wiretapping in LAWNs. Building upon this architecture, we formulate a max-min secrecy-rate problem that jointly optimizes AP mode selection, receive combining, and AN covariance design. This tightly coupled and nonconvex optimization is tackled by first deriving the optimal receive combiners in closed form, followed by developing a penalty dual decomposition (PDD) algorithm with guaranteed convergence to a stationary solution. To further reduce computational burden, we propose a low-complexity sequential scheme that determines AP modes via a heuristic metric and then updates the AN covariance matrices through closed-form iterations embedded in the PDD framework. Simulation results show that the proposed flexible-duplex architecture yields substantial secrecy-rate gains over CF systems with fixed AP roles. The joint optimization method attains the highest secrecy performance, while the low-complexity approach achieves over 90% of the optimal performance with an order-of-magnitude lower computational complexity, offering a practical solution for secure uplink communications in LAWNs.