Yes, Amazon Freetime Unlimited content can be managed via web. The web UI for managing content can be accessed by going to http://my.amazon.com/family.
Once there, you can customize your child’s account. You can set age filters, pick which skill sets will be available for each child, set time limits for app usage, and manage the books, videos, apps, and other content available for your child.
You can also add or delete specific apps from the Dashboard. You can easily search for and find content that’s appropriate for each child.
In addition, if you want to view reports on your child’s app and content usage, you can do so right from the Dashboard.
Therefore, you can easily manage your Amazon Freetime Unlimited content via web.