How to approve iPhone if you have no other device?

I had the same problem. I actually had an old ipod associated with my account that I didn't realize and had to remove it.
Go to: https://appleid.apple.com And choose "Manage your Account".
Look at your devices and see if you have any old devices. If so, remove them. That is what worked for me.

I just sorted this issue out on my phone with somebody from Apple customer service.

All you have to do is to go to the bottom of the page where it says something like: "Can't approve this iphone?", click on this option and you will have to reset your encrypted data. Don't worry because you will lose nothing. This encrypted data is connected to your Keychain option in your iphone which stores your passwords you use to automatically loggin into different apps. You will just be asked to re-loggin, if this will be the case, when you will use an app for which you've saved the loggin password. Once you followed all steps in resetting your encrypted data you will be redirected back to the original screen and you will have to click again on "Continue", enter again your password for your Apple ID account and this should be all. Your phone should work and it will be approved.

I hope this helps.