Question

When a user runs my app (iOS or Android), can I automatically get their phone number and contact details for back up?

Answer 1

I can’t vouch for Android but for iOS the answer is a definite no. Here’s what Apple will say when they reject your app:

For security reasons, iPhone OS restricts an application (including
its preferences and data) to a unique location in the file system.
This restriction is part of the security feature known as the
application’s “sandbox.” The sandbox is a set of fine-grained controls
limiting an application’s access to files, preferences, network
resources, hardware, and so on.”

The device’s phone number is not available within your application’s
container. You will need to revise your application to read only
within your directory container and resubmit your binary to iTunes
Connect in order for your application to be reconsidered for the App
Store.

See Programmatically get own phone number in iOS for additional notes.