Seems to be a similar problem like this one here:
Vulkan seems to need DRI3, which is not enabled by default. If you are really sure, that your Intel Chipset supports vulkan, then add this
Section "Device"
Identifier "Intel Graphics"
Driver "intel"
Option "DRI" "3"
EndSection
to your /etc/X11/xorg.conf.d/20-intel.conf. If not there, create one and reboot. Check vulkaninfo again.
Alos keep sure that you have installed vulkan-intel and vulkan-icd-loader.