It is absolutely safe to use Circle.us to manage your multiple Amazon accounts. By using Circle.us, you grant our web server to connect your Amazon stores through Amazon Web Services.
Amazon will not see your personal information or your computer configuration like IP addresses and Mac addresses. Circle.us, as a stand-alone company, is not affiliated with Amazon by any means, and we will never share any information with Amazon.
Therefore, your multiple accounts will stay unlinked and covered from Amazon's prying eyes!