Best practice for private key backup flow on mobile

The mobile app I'm working on is using end-to-end encryption algorithm. User creates a private key to read data that is saved on the server. The key is being stored on a device and can be exported to a file.

When user chooses to use app on a different device, he/she should be able to import the private key in order to read out the encrypted data.

What could be the best, and still, safe experience for a user to create a backup of the private key file?

One of the options could be exporting the key to the cloud. The key could be also printed out, although the limitation is the mobile – it can get tricky for some users to print out directly from the device.

Do you know any apps, or solutions that could nicely solve this problem?