CloudVeil does not have any filtering products for the Kindle Fire at this time. However, the Kindle Fire can be locked down completely as shown in the following guide. This guide was created using the Kindle Fire 7.
To keep the device secure, the WiFi should remain off unless needed for downloading books. Turning the WiFi on will require the parental controls password. While the WIFi is on, there is access to music etc even with parental controls enabled, but the builtin web browser will be disabled.