First: What version of Mendix are you using? Next: the problem is in the application that makes the request. Or more specifically, your services receives calls fine when called by Postman, so the question is: what is different between the Postman-call and the outsides applications calls?
Ok, so I was able to reproduce the problem from Postman. When I carefully inspected the headers coming from the service, i see they are sending a header for Content-Type: x-www-form-urlencoded, yet they are sending JSON in the body. When i forced a header like that from Postman with a JSON body, the content parameter in Mendix is empty. Not sure this is best practice from Slack's end but it is causing an issue here.
UPDATE:
Figured it out. Slack is responding with a www-form-urlencoded single parameter of "payload" with the JSON in the payload parameter.