iPhone can not upload notes to iCloud
I bought iPhone 7 a few days and got exactly the same problem. My old iPhone 5S still syncs perfectly but new one doesn't.

Have done everything: logged out Apple ID and in again, turned off iCloud Notes syncing and then on again, still nothing. Even set my new phone up as a new iPhone but the Notes app is still not syncing with other devices where it works perfectly. I can see notes made on other devices but edits made on iPhone 7 are not showing up on my old iPhone, iPad and Macbook Pro.

I tried all these things here but mine isn't still working - maybe it works for you: http://www.idownloadblog.com/2016/12/19/icloud-notes-not-syncing-fix/