Please check https://forum.syncthing.net/t/dual-boot-ntfs/16683/9 on how to make Syncthing portable.
However, in your case, it seems that you should just store those folders in a location that can be accessed from both OSs and then add them to Syncthing in each of them separately. When doing so, make sure to enable “Ignore Permissions” in the folder advanced settings as well.