If you are using Authy for Two-Factor Authentication:
As soon as you replace your smartphone, you can simply reset your phone at Authy.
If you are using Google Authenticator or TOTP for Two-Factor Authentication:
When you first setup Two-Factor Authentication, you received a backup code in case you lost your phone.
On your new phone, enter the backup code into Google Authenticator or into the TOTP app you were using in order to sync it with your Cloudflare account.
On Google Authenticator, install Google Authenticator. Then open the app and click 'Begin Setup'.
Choose 'Manual Entry'.
Enter your Cloudflare email and your two-factor backup code. Check Time-based.
If you remain unable to log in to your Cloudflare Account due to 2-Factor Authentication issues, contact email@example.com