I FINALLY HAVE THIS SOLUTION TO THIS ANNOYING CYCLICAL iCLOUD ISSUE!!!
After you've reached the point that you're being prompted to enter a password and verification code... and are having no luck bc theres no place to enter the V code after you enter your password AND
1. You've already tried entering them on the same line as someone else suggested: "password123456" (password+6 digit v code on the same line). But it keeps returning "Password Incorrect" in alarming red letters!
Your problem may be the same as mine: WRONG V Code!
I was repeatedly going to My Apple ID on my Mac when Id get a note that my iCloud account couldn't get online. I'd enter my name & password, wait for the 2 factor verification ping to come thru my iPhone then enter that 6 digit code into the 6 spots to reopen Apple ID on my Mac. Then I'd rush to enter the same v code into the password sequence in the iCloud error window with my password. There was NO OTHER PLACE to get a verification code, so I was caught in this cycle for a week-- until I happened to be messing with my email servers and discovered this lovely trick:
Go to SETTINGS, then MAIL, then ACCOUNTS, then iCloud, then click on YOUR NAME(iCloud account)@ME.COM which should already be loaded at the top of your iPhone, then click on, PASSWORD & SECURITY, scroll down... wait for it... GET VERIFICATION CODE!!! Its right there under your nose buried in the 5th circle of Dante's ****.
Now return to your flaccid iCloud window, enter "password123456" (password+6 digit v code you just retrieved on the same line), and Bingo, you're in!
You're welcome, Mac Users of the World, you're welcome...ks