There are currently several backup strategies:
1. No backup...
2. Export as QR-code...
3. Export private key to clipboard...
4. Export to SD card...
I would suggest adding a "share" option. Provided my understanding of it is correct, that should allow you to export the key to a particular application, rather than directly exposing it to all running applications like the clipboard option, or all programs with SD card access like the file option.
Interesting idea. On Android there is a mechanism to share content with various apps based on content type. For instance you can click on your address on the main view and share it as text with various apps accepting text.
To do that safely with key export (as a text or a JPG image) I would like to first have BIP 38 implemented (export with encryption) with an app generated secure passphrase. Something to look into going forward.