I am on a ubuntu 16.04 machine with a Radeon HD 8670M card. I had installed the examples provided by LunarG on their github repo and they compiled and executed successfully.
To teach myself how to set up a basic project I was following the introductory tutorial at https://vulkan-tutorial.com. I printed out the device name after running the function vkEnumeratePhysicalDevices and it only returned the integrated Intel Graphics card.
My lspci output lists the AMD card as the display controller instead of the VGA controller. I tried updating my drivers and researching a bit more about this specific issue with integrated cards without much luck.
I have the cards properly configured in xorg.conf.d, in the files 20-intel.conf and 21-radeon.conf. I am not sure if this decided the priority order but on inspecting the xorg log file they are loaded with DRI3 enabled, which I am assuming is a prerequisite for being a suitable device.