If you want to do this, then I would suggest storing both the binaries, config, and database all in a folder on that partition, and then running everything from there. This way you will have a self-contained portable installation. I would also disable automatic upgrades, because you do not want to have different versions of Syncthing messing around with the same database and config.
For example, if your NTFS partition is D:\ in Windows, then place syncthing.exe in a folder called D:\Syncthing, and then run it using syncthing.exe -home=home from inside that folder. Then, you can do the same using the Linux binary, e.g. syncthing -home=home, etc. Also, always make sure that both the Windows and Linux binaries are the exact same versions.
Ideally, you should also use relative paths for all your Syncthing folders too, so that they can persist across the different operating systems. Syncthing accepts forward slash / path separators in Windows too, so I would suggest using these everywhere.