In a large dry skillet over medium-low heat, toast the cashews and coconut flakes, stirring until fragrant, about 3 to 5 minutes. Pour mixture into a bowl to cool.
Return pan to the heat, and add sesame and coconut oils, then stir in asparagus. Season lightly with salt and black pepper. Cook asparagus until crisp-tender, 3 to 7 minutes depending on how thick they are.
Stir in the soy sauce, lime juice, nut mixture and red-pepper flakes. Taste and season with more salt and red pepper, if needed. Transfer asparagus mixture to a serving dish and serve.