Vane assemblies for turbine engines are described. The vane assemblies include a vane having an internal cavity and a vane platform and a vane rail defining, in part, an outer diameter supply cavity. A blade outer air seal support (BOAS support) is arranged adjacent the vane and engages with a portion of the vane, the blade outer air seal support having BOAS support rail, and a BOAS supported on the BOAS support and engaging with a portion of the vane. The BOAS support includes a first cooling flow aperture configured to enable a cooling flow to cool at least the BOAS and a second cooling flow aperture formed in the BOAS support rail. The vane rail includes a third cooling flow aperture to form a cooling flow path through the second cooling flow aperture and the third cooling flow aperture to fluidly connect to the outer diameter supply cavity.