The vector field method was originally proposed to guide a single fixed-wing Unmanned Aerial Vehicle (UAV) towards a desired path. In this work, a non-uniform vector field method is proposed that changes in both magnitude and direction, for the purpose of achieving formations of UAVs. As compared to related work in the literature, the proposed formation control law does not need to assume absence of wind. That is, due to the effect of the wind on the UAV, one can handle the UAV air speed being different from its ground speed, and the UAV heading angle being different from its course angle. Stability of the proposed formation method is analyzed via Lyapunov stability theory, and validations are carried out in software-in-the-loop and hardware-in-the-loop comparative experiments. Note to Practitioners - The software-in-the-loop and hardware-in-the-loop experiments, which are done with PX4 autopilot software and hardware, show that the proposed method can be implemented on board of UAVs and integrated with the control architecture of existing autopilot suites. Comparisons with standard formation algorithms show that the proposed method is effective in achieving formation in different path scenarios.