For openSUSE Tumbleweed run the following as root:
zypper addrepo https://download.opensuse.org/repositories/devel:Factory:git-workflow:staging:jengelh:vulkan-validationlayers:1/openSUSE_Tumbleweed/devel:Factory:git-workflow:staging:jengelh:vulkan-validationlayers:1.repo
zypper refresh
zypper install vulkan-validationlayers
For openSUSE Slowroll run the following as root:
zypper addrepo https://download.opensuse.org/repositories/devel:Factory:git-workflow:staging:jengelh:vulkan-validationlayers:1/openSUSE_Slowroll/devel:Factory:git-workflow:staging:jengelh:vulkan-validationlayers:1.repo
zypper refresh
zypper install vulkan-validationlayers