I got close. So I started by copying the way Nagios does its integration with FreshService - since Fresh actually has a pre-built plugin for Nagios, and Checkmk uses the same OMD monitoring platform as Nagios, I thought it would be a breeze. Not so easy, although I did succeed in getting it to log a ticket in Fresh! The data was all munged up though, and I suspect its because CMK is not sending the payload in JSON format, which Fresh is setup to receive.
I need to find out a way to get CMK to send the alert payload as JSON, but reeeeeally struggling. There doesnt seem to be many people on here doing similar things.
The way I got it to partially work is to essentially copy the Nagios commands over to CMK using a custom bash script in the ~/local/share/check_mk/notifications folder. I created 2 scripts, 1 for host alerts, and 1 for service alerts (exactly as setup in Nagios).
The script is essentially a curl post containing the API URL, auth header and payload data from the alert.
I can then create a new notification rule using this method, and bingo, CMK is logging tickets in Fresh. But the data is unintelligible, since I believe the payload is not coming through in JSON, OR the payload data uses completely different payload headers to Nagios.
Ideally I need to see what the payload is, but really struggling to find a way to do this, as there is not much information on the forums for it, and they seem to be pushing us to pay for some consultancy hours (which is not cheap!!). We are ent-edition customers btw 
If anyone can help further that would be amazing.