There are a few options to deploy Kong as your API Gateway:

Kong can work as an Ingress Controller for your Kubernetes cluster and run plugins for your traffic at the Ingress layer. Refere to the repo for more details: https://github.com/kong/kubernetes-ingress-controller

You can simply deploy it as an application using the Helm chart: https://github.com/helm/charts/tree/master/stable/kong

If you're using Kubernetes, you should check out Ambassador. Declarative syntax, no database (persists to etcd), very high performance, built on Envoy Proxy.

There's a helm chart for that :) https://github.com/helm/charts/tree/master/stable/kong