At the moment of writing, docker checkpoint feature is still in experimental phase so there is no official (HTTP) API documentation. Nonetheless, there is an endpoint on the docker daemon that can accept an HTTP request, as it is the one that docker cli uses.
Based on the related docker source code it should be something like
sudo curl -X POST --unix-socket /var/run/docker.sock http://localhost/v1.32/containers/20fb4f16ff10/checkpoints
but this does not work. Any ideas what I may be missing?