I’m offering a bounty of 600 US dollars for proper write support to external SD cards (e.g. /storage/extSdCard on my Samsung Galaxy Note 4) in Android 5.0 and later without requiring rooting the device. As per this recent discussion:
doing so appears to require using Android’s Storage Access Framework.
This bounty is payable via PayPal to whoever adds the necessary feature to the Syncthing client for Android, once it’s included in a mainline release (i.e. not a special one-off version), as long as this happens before the end of 2015.
Others who would like to see this feature (I know you’re out there!) are invited to contribute to the bounty.
You seem to have answered the general “how do I write to an SD card on Android” in hunt for the bounty, which is not the context in which the question was asked. New users with multiple links run the risk of getting spam flagged. In this case I’m inclined to agree.