Yes, that laptop GPU Card does support Vulkan according to its Specs at this tech website: AMD Radeon R8 M535DX Specs | TechPowerUp GPU Database
Download free program GPU-Z and see if Vulkan is checked marked at the bottom of GPU-Z image like mine:
The API's I have checked mark should be checked mark for your AMD GPU Card also. The others are for Nvidia GPU cards.
If Vulkan is not check marked than you have a corrupt AMD Driver installation that enables the API in your GPU card.