remote syslog

You can install the rsyslog add-on from the LE add-on repo.

You can
1) Use "paste" as

cat /storage/.kodi/temp/kodi.log|paste

and use the url
2) You COULD use the Kodi addon "Log Uploader" but it is reported as BROKEN.
3) Use any number of websites like pastebin.com to upload.

There's a paste function in LE 8.0 settings add-on that sends logs to sprunge.us and shows the URL on-screen, but that doesn't address the OP's requirement of sending to a syslog server.