Transport in nonergodic dynamics is a fundamental topic in quantum many-body physics. Integrable systems, due to their infinite number of conserved quantities, exhibit unique ballistic transport properties. In this work, we systematically investigate an integrable model of cold atomic gases—the one-dimensional p-wave Fermi gas. Although the theoretical description of this model has been extensively studied, its ballistic transport properties have not yet been fully elucidated. Within the framework of thermodynamic Bethe ansatz (TBA) equations and Generalized Hydrodynamics (GHD), we derive an expression for the Drude weight that characterizes ballistic transport and establish a universal relation linking it to basic thermodynamic quantities such as particle density, energy density, and entropy. This relation holds in all integrable systems satisfying Galilean invariance. Under equilibrium conditions and for weak interactions, we obtain the low-temperature thermodynamic quantities and the Drude weight via Sommerfeld expansion, and further explore the dependence of the Drude weight on both interaction strength and temperature. For non-equilibrium states, we analyze the evolution under three protocols—tilted potential, local chemical potential difference, and local temperature difference—all governed by the GHD equations. Numerical calculations of the transport coeffcients in steady states agree perfectly with the results obtained from integral expressions, further validating the reliability of the theoretical framework. Furthermore, using the polylogarithm function, we derive a universal scaling equation for the transport coeffcients. It is found that the transport coeffcients exhibit clear scaling behavior near the quantum critical point of the transition from the vacuum state to a finite-density Fermi state, and their temperature dependence is consistent with the universality class characterized by dynamical exponent z = 2 and correlation length exponent ν = 1/2, thereby confirming the self-consistency of the theory. This work not only provides a systematic theoretical framework for understanding ballistic transport in one-dimensional p-wave Fermi gases but also deepens the general understanding of transport properties in one-dimensional quantum continuum integrable systems.