How do I approve an iPhone?

Is you keychain enabled? See the pic below, is this your situation?

Try these steps in order:

1. Turn off iCloud Keychain on both the devices
2. On your iPhone, go to Keychain and tap Approve with Security Code
3. When prompted for the 4-digit iCloud Security code tap Forgot Code
4. Simply follow the prompts and steps to reset the code
5. Now this device will have iCloud Keychain enabled and working
6. Now on your second device, enable iCloud Keychain
7. You should get a notification on the first device about this activity. Enter your iCloud / Apple ID password when asked
8. iCloud Keychain should now be enabled

This is almost certainly a keychain issue. Try these steps:

1. Turn off iCloud Keychain on both the MacBook and iPhone.
2. From your iPhone, go to Keychain and tap Approve with Security Code.
3. When prompted for the 4-digit iCloud Security code tap Forgot Code.
4. Follow the prompts to reset the code.
5. Now this device should have iCloud Keychain enabled and working.
6. Now from your MacBook, enable iCloud Keychain.
7. You should get a notification on the iPhone about this. Enter your iCloud password in the prompt.
8. iCloud Keychain should now be enabled.

Most likely the process will stop "Approve your device" notifications!