Hello from Amazon Selling Partner Support,
I understand that you wanted to close your selling account but unable to log-in due to the required two-step verification.
To address your inquiry, we highly recommend you to go through account recovery first so that you'll be able to log in to your selling account and have an access to this tool (see link below) to close your account: https://sellercentral.amazon.com/help/hub/solution/DA_CloseAccount2
To process your account recovery, please follow the steps below:
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Attempt to sign in to Seller Central, and click "Didn't receive the code?" on the bottom of the page where you enter your authentication code. Select your backup method to receive codes.
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If you do not have access to your backup device, you will need to go through the account recovery process. Visit https://www.amazon.com/gp/help/customer/display.html?nodeId=202073840
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This will require you to submit a copy of your government-issued identification to confirm your identity. This usually happens within 12 hours, but it could take 1-2 days.
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Once your account is recovered, you will be required to enable Two-Step Verification again. You can enter a new primary and backup method for receiving your authentication codes, which you can change at any time on the Advanced Security Settings page. When you re-enable Two-Step Verification, you may notice that your previously designated phone numbers are populated in the fields.
If the numbers are no longer valid, visit Two-Step Verification (2SV) Setting: https://www.amazon.com/a/settings/approval and delete the outdated information.