How to approve an iPhone (Mac and iCloud)

I was having this same problem. What I ended up doing was turning on the key chain on my iPad.( the device I was trying to use to approve my iPhone.) I was then asked to go on to another device to approve my iPad. At the bottom of the screen it had an option and blue text that said cannot approve this device. I clicked that and it asked me if I wanted to reset my encrypted data and I click to reset. It warned that it may delete all my passwords and everything that go along with the keychain but I hit reset anyway. Then with my fingers crossed I turned the key chain on my iPhone on. It asked for my passcode and then said I needed to approve my device. This time I was promoted to approve the device by entering my password on my iPad. Problem solved. Oh and by the way all my passwords etc. where still there.