file:///usr/share/kibana/src/ui/public/assets/favicons/image.png
I don't think that's what you want, since file: will point to your local machine, not the file on the server. Kibana should be hosting it, so you should be able to access it from <your kibana hostname and port>/ui/favicons/image.png, and then the correct why to use that in markdown would be:
<your kibana hostname and port> there would be http://localhost:5601 or https://internal.tld or whatever you use to connect to Kibana.