I don't know of any existing solution to this, but it shouldn't be too hard to create something like this. Let's suppose you're using Nextcloud/Owncloud, then you could create a share in which you allow uploads. Using curl (which is already included in KoboCloud) you can then upload any file to that share. To summarize:
- Create public share allowing uploads
- Use the udev-trick by KoboCloud to run your upload script
- Add some logic to find your screenshots (Mostly look for /mnt/onboard/Screenshot*.png) files
- Upload them using curl (comes down to something like curl -T $file -u "$FOLDERTOKEN":"$PASSWORD" "$CLOUDURL/$PUBSUFFIX/$file"
Hope this helps to get you going.