I am unable to throw a video to a DLNA device using the built-in tablet Camera application.

The built-in Camera application has the ability to throw pictures to a DLNA device, but does not have the ability to throw video files.

Instead of trying to use the Camera application, use the built-in DLNA feature to throw pictures or videos from the tablet to another DLNA enabled device.

NOTE: There may also be additional applications available from the Google Play Store that will allow you to throw saved video files to the DLNA device.