iCloud Keychain sync: How to determine current sync status or force a sync (without removing and adding)?
There are no built-in OS X tools designed explicitly for showing you iCloud synchronize information. In easy to read way.

However, you can track connections to Apple's iCloud servers, measure traffic flow, and disk access. 

These metrics will provide some insight but they will not provide expected duration's or percentage complete measures.

To explore the data flow, explore the OS X's built-in tools like lsof and netstat.