Generate a security token using a admin token?

I'm genuinely curious about the reason you're trying to use the token API. A lot of the time when I get questions about how to use it, it turns out that it's not the right fit for the problem that the person wants to use it for.
If you do have a particular reason for wanting to use this API, then I'd love to understand what it is.

Reading between the lines, I think you are being thrown off course by the error message that Elasticsearch returns if you fail to provide authentication credentials for your request ("missing authentication token for REST request"). That error does not specifically refer to tokens from the token management API, it refers to any credentials. You could provide an oauth token, but you can also provide a username+password for native Elasticsearch or LDAP users, or a SSL PKI certificate.