I use Syncthing on two Android devices, a phone and a tablet. On the phone (a Moto G4), it works flawlessly, but that's because I'm only using internal storage. I sync the phone's pictures and a few folders that have notes (recently replaced Evernote with Orgzly to do this).
On the tablet (LG GPad 8.3), I have 16GB of internal memory and a 64GB micro SD. This is where I have the most problems, and I don't think it's the fault of Syncthing; rather, I think it's a limitation imposed by the design of Android.
To get this to work at all, I must have the tablet rooted and have used the SD Fix app to restore pre-Kit-Kat functionality to the SD card. Otherwise, Android itself limits access to the SD card. My tablet is running Lollipop, and this seems to work (see below), but I understand further changes were made to the way SD cards work in Marshmallow and Nougat, so this could still be problematic in newer versions of Android.
Even with these changes, I experience the UI lockups noted by others above. The binary keeps running and syncing, but the UI becomes unresponsive and Android asks me if I want to kill the app. This means I wind up only starting Syncthing when I know something needs to be synced, and then I reboot the tablet once I see that it has synced.
The only difference between the two devices is the use of the SD card. I don't think this is the fault of the Syncthing android app. I think Google is going in a particular direction: if you want lots of storage, buy a more expensive device that includes it internally. For me, this is the wrong direction: I want to stick a big SD card in there and sync lots of stuff to it, because I basically want an ultra-portable computer, not a streaming-media consumption device. That's why I have the keyboard case and everything.
For this reason, I'm strongly considering an Ubuntu tablet next. I think whatever the Syncthing Android developers do, they will be fighting an uphill battle with the platform itself. @Nutomic and crew have done a fantastic job in their spare time getting Syncthing to work on this platform, and they should be applauded for their efforts. But ultimately, I think Google, despite the low cost of local storage, is doing what they can to push everybody into the cloud, and that's a strategy that I, and I suspect many people who use Syncthing, don't agree with.