How can I get a verification code if my iPhone is broken?

You can try this method.

If your Apple ID is locked or disabled

If you or someone else enters your password, security questions, or other account information incorrectly too many times, your Apple ID automatically locks to protect your security and you can't sign in to any Apple services.

How to unlock your Apple ID

If you use two-factor authentication, you need a trusted device or trusted phone number to reset your Apple ID password and unlock your account. If you have a recovery key, you can also use it to help you regain access to your account.

If you see a message that says your account has been disabled in the App Store and iTunes Store, contact Apple Support for help. 

If your Apple ID is locked for security reasons, you might see one of these alerts:

• “This Apple ID has been disabled for security reasons”
• "You can't sign in because your account was disabled for security reasons"
• "This Apple ID has been locked for security reasons"

If you can't unlock your Apple ID

If you use security questions with your Apple ID, or if you don't have access to a trusted device or phone number, go to iforgot.apple.com. Then you can unlock your account with your existing password or reset your password. After multiple unsuccessful attempts to unlock your account, your Apple ID will remain locked and you can try again the next day.

Published Date: April 29, 2020

https://support.apple.com/en-us/HT204106

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See these reads on two-factor authentication. I assume he is using this security system. See the account recovery part especially.

Get a verification code and sign in with two-factor authentication https://support.apple.com/en-us/HT204974  Below is an excerpt, but read the whole document.See the bold italics below.

“Whenever you sign in with your Apple ID on a new device or browser, you'll confirm your identity with your password plus a six-digit verification code. There are a few ways you can get a verification code. You can use the code displayed on your trusted device, get a text or phone call, or generate a code from your trusted device [see the additional information in the article].” A trusted device is an iPhone, iPad, or iPod Touch with iOS 9 and later or a Mac with OS X El Capitan and later that you've already signed into using two-factor authentication.

Account Recovery—Two-Factor Authentication (i.e., Recover your Apple ID when you can’t reset your password  https://support.apple.com/en-us/HT204921

“If you can’t sign in, reset your password, or receive verification codes, you can request account recovery to regain access to your account. Account recovery might take a few days or longer, depending on the specific account information you can provide to verify your identity. “After you request account recovery, you'll get an email with a confirmation of your request and the date and time of when you can expect to regain access.” … When the wait period is over, Apple sends you a text or automated phone call with instructions to regain access to your account. Follow the instructions to immediately regain access to your Apple ID.”