Go to Settings > Security and toggle on Unknown Sources to allow the installation of the APK file [1].
This was the secret sauce of KingRoot. It didn't use a single exploit; it had a database of hundreds of them. It cycled through known vulnerabilities in the Linux kernel, throwing code at the wall until something stuck. kingroot+520+new
This article breaks down everything you need to know about this elusive software version, its features, risks, and alternatives. Go to Settings > Security and toggle on