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I had applied two-factor security settings on my iPhone (model 5S).
That phone went out of order and its not turning ON.
How should I get access to my stored data and how should I get that double check (two factor code) while my cell phone is not working.
iPhone 5s, iOS 12
See the following from Two-factor authentication for Apple ID - Apple Support
What if I can't access a trusted device or didn't receive a verification code?
If you're signing in and don’t have a trusted device handy that can display verification codes, you can have a code sent to your trusted phone number via text message or an automated phone call instead. Click Didn't Get a Code on the sign in screen and choose to send a code to your trusted phone number. You can also get a code directly from Settings on a trusted device. Learn how to get a verification code.
If you use iOS 11.3 or later on your iPhone, you might not need to enter a verification code. In some cases, your trusted phone number can be automatically verified in the background on your iPhone. It’s one less thing to do, and your account is still protected with two-factor authentication.
If I can't sign in, how do I regain access to my account?
If you can’t sign in, access a trusted device, reset your password, or receive verification codes, you can request account recovery to regain access to your account. Account recovery is an automatic process designed to get you back in to your account as quickly as possible while denying access to anyone who might be pretending to be you. It might take a few days—or longer—depending on what specific account information you can provide to verify your identity.
If you generated a recovery key, you can use your recovery key to regain access to your account instead. Learn more about using a recovery key.
See the following from Two-factor authentication for Apple ID - Apple Support
What if I can't access a trusted device or didn't receive a verification code?
If you're signing in and don’t have a trusted device handy that can display verification codes, you can have a code sent to your trusted phone number via text message or an automated phone call instead. Click Didn't Get a Code on the sign in screen and choose to send a code to your trusted phone number. You can also get a code directly from Settings on a trusted device. Learn how to get a verification code.
If you use iOS 11.3 or later on your iPhone, you might not need to enter a verification code. In some cases, your trusted phone number can be automatically verified in the background on your iPhone. It’s one less thing to do, and your account is still protected with two-factor authentication.
If I can't sign in, how do I regain access to my account?
If you can’t sign in, access a trusted device, reset your password, or receive verification codes, you can request account recovery to regain access to your account. Account recovery is an automatic process designed to get you back in to your account as quickly as possible while denying access to anyone who might be pretending to be you. It might take a few days—or longer—depending on what specific account information you can provide to verify your identity.
If you generated a recovery key, you can use your recovery key to regain access to your account instead. Learn more about using a recovery key.
How to get access on two-factor code when master device is lost / out of order.
