The short answer is no.
Syncing Amazon reviews doesn't violate their Terms of Service.
There are a few specific guidelines you should ensure you are following in order to stay compliant.
Here are a few things to keep in mind Amazon reviews must:
Not be incentivized
Be genuine customer reviews
From customers who have actually purchased (no solicitation from friends, family, or employees)
Not be automated
Don't use automated tools to post or generate your Amazon reviews