In this scenario, the best solution is an authenticator app. Authenticator apps don't require cellular network coverage in order to generate a code.
For more information, see Use an authenticator app for Two-Step Verification.
If your phone is lost or stolen, contact your carrier immediately and ask them to block or suspend your line, until you can figure out what happened.
To gain access to your seller account, try logging into Seller Central and click Didn't receive the code? on the bottom of the Two-Step Verification page. Select your backup method for receiving your code.
If you don't have a backup device and can't change your settings, you'll need to go through the Two-Step Verification Account Recovery process. This process requires you to submit documentation verifying your identity. Once verified (usually within 12 hours), Two-Step Verification will be disabled so you can log in. On your next login, you will be required to set up Two-Step Verification again, this time using devices that you have access to.
There are several things that you can do to ensure you always have access to your account:
Click the Didn't receive the code? link on the webpage where it asks you to enter your code. This lists any backup methods you designated when you set up your account. You can also choose to have a voice call to your cell phone in case the SMS text didn't arrive.
If you don't receive a code during registration, check that the phone number you provided is correct. Make sure the phone number includes a region code, and your cell phone can receive SMS text messages.
This is usually an issue with your browser settings. Clear your cache and cookies, then try logging in again.
If this doesn't work, try requesting a code on your backup method by clicking the Didn't receive the code? link on the Two-Step Verification page. This will list any backup methods you designated when you set up your account. You can also choose to have a voice call to your cell phone in case the SMS text didn't arrive.
If you have an issue receiving a code during registration, make sure that the phone number you provided is correct. Make sure that the phone number includes a region code, and that your cell phone can receive SMS text messages.
If you can log in to Seller Central without seeing a message saying that Two-Step Verification is a requirement, then you have Two-Step Verification enabled.
In Seller Central, go to Settings > Login Settings > Advanced Security Settings > Edit to view your settings. Click the Change link next to the item you want to change and follow the on-screen instructions to change and save your Two-Step Verification Settings.
You can also access your Two-Step Verifications settings on the Advanced Security Settings page on the Amazon Retail site.