This is something we’ve been investigating since the app’s inception and we continue to investigate constantly. Syncing is a very difficult problem to solve, especially in regards to handwritten notes which can be combined with images and text. I don’t have any kind of ETA for when syncing will be supported, but rest assured this is a high priority for us. We appreciate all your feedback on this idea.Michael commented
Just subscribed to premium, and surprised to find this still hasn't been implemented. A rough workaround, for those that would like same ability to synchronise between devices, is to manually change the "Device name" within the Backup and Restore settings to be the same for both devices. I've used "google Combined Devices" on my phone and Chromebook, so both devices will look into the same linked Dropbox account for backup. Backup from one device, then restore on the other device.