The need for better aeroengine efficiency and fuel burn savings can be addressed by increasing turbine cycle temperatures. New cooling technologies such as emerging double skin transpiration (DST) systems, are essential for preserving the integrity of metallic parts if operating temperatures are to be increased beyond current levels. Their implementation, however, requires complex architectures with detailed features such as inclined film holes that raise local stresses. Our aim is to accelerate the implementation of DST systems in turbomachines, by providing an understanding of their implications on thermal stresses and the creep-fatigue failure processes. By using geometric, temperature field and nickel alloy material property idealizations, we generate both theoretical and Finite Element (FE) solutions for the thermal stress field and the critical cyclic strain range. Theoretical stress analysis and a local approach to failure lead to life predictions that are in reasonable agreement with inelastic cycle-by-cycle FE analysis, suggesting that analytical approaches can be useful for immediately identifying the significance of the various geometric features and thermal loading parameters. Film hole locations are predicted to fail under low cycle fatigue, suggesting that optimizing hole inclination, hole shape and other important geometric features is critical.