By default, all cookies website create in Private mode is cleared when the Private window is closed. There is no way to block cookies for specifically Private mode, but you can block cookies for Instagram for both Normal and Private windows: 1. Go to '''about:preferences#privacy''' 2. Select '''Manage Exceptions''' under the section '''Cookies and Site Data''' 3. Input '''www.instagram.com''' in the field and select '''Block''' Now cookies and data from Instagram should be blocked everywhere.