I had very little luck with the various Apple approved methods of solving this issue. Nothing would appear on my Macbook’s iCloud Keychain even after very elaborate tricks to turn iCloud Keychain off and on.
What did work was that in frustration I airdropped a single web site password from my iPhone to my Macbook. Subsequently every password appeared in iCloud Keychain on my Mac and subsequent passwords synced over iCloud. (Like the very password saved on this site I just made on my iPhone 5 minutes ago synced over iCloud to the MacBook soon thereafter).
I don’t know why this worked or if it will work for others but worth trying!