To resolve the issue of your Kroger app repeatedly asking for your email and password after getting a new phone, follow these detailed steps:

1. Check Internet Connection: Confirm that your new phone is connected to a stable Wi-Fi or mobile network. A poor connection can lead to login issues.

2. Install Latest Kroger App Version: Ensure you have the latest version of the Kroger app installed. You can do this by visiting the Google Play Store, searching for the Kroger app, and updating it if necessary.

3. Clear App Cache:
- Go to your device's Settings.
- Select Apps or Apps & Notifications.
- Find and tap on the Kroger app.
- Tap on Storage and then select Clear Cache. This can help solve issues with the app misbehaving.

4. Re-login to the App:
- Open the Kroger app.
- Enter your email and password to log in again.
- If prompted to save your login information, select the option to remember your credentials. This may prevent the app from asking for login details every time.

5. Check for Multi-factor Authentication: If your account has multi-factor authentication enabled, ensure you've completed the necessary steps to verify your identity. If you're having issues, you may need to reset your multi-factor authentication - learn more.

6. Reset Password (if needed): If you suspect that your password might be causing issues, you can reset your password:
- Go to the Kroger sign-in page.
- Click on Forgot Password? and follow the prompts to reset it - learn more.

7. Reach Out to Kroger Support: If the issue persists after following the above steps, it may be helpful to reach out to Kroger customer support. You can find assistance through their Account Troubleshooting FAQs which provide answers to common problems - learn more.

8. Consider Device Compatibility: If your new phone has specific compatibility issues that prevent the app from functioning properly, consult the Kroger app specifications or support for further insights.

These steps should help you resolve the login issue on your Kroger app. If you continue to experience problems, detailed troubleshooting through customer support may be needed.