How to backup on Mobile
Sadly there is no official way to do a backup of your data on Android or iOS. The only way to do a backup of your BAT is to have it connected to Uphold or Gemini.
iOS
You can go Hamburger Menu → Bookmarks to then Export Bookmarks or Import Bookmarks but that’s the only thing you can import/export or have as a backup. All other information needs to be done using Sync.
Android
Has an option in Settings → Passwords to Export Passwords but there’s not an option to Import Passwords. Therefore, only way to do anything is via Sync.
The Mobile Product Manager recently spoke that they were working on developing further options. Until then, the ONLY real form of backup for Mobile is Brave Sync. However, that’s not officially supported and the sync phrase changes daily. This means it’s not a long term or reliable form of backup.
To set up sync, go to Settings → Sync and then Start a new Sync Chain if you don’t have one yet. Then make sure you choose to sync everything and write down the code.
To then have all the data moved to new or formatted device, you’d then go to Settings → Sync and then I have a Sync Code where you’d put in the code you had just written down.
–NOTE–
I just want to emphasize again that the Sync Code changes daily. Also, as the developers have said:
Warning: Brave does not officially support using the Sync code as a backup and you should not rely on this continuing to work in to the future.
It should be fine as long as you have other devices on the sync chain or if you can set everything up and transfer right away. But unfortunately there’s no satisfactory way to do a backup of Mobile data at this time.