Best How To :

I agree with @Daan's comment.

Add a new column in your database (current_featured_id), it could be TINYINT with default value of 0. If a video is featured the row will have a 1 in the current_featured_id column.

In terms of the actual cron job, add in your crontab a command to run the function once a week * 0 * * 0 featured_vid (runs every Sunday at midnight)

function featured_vid() {
     //get the current featured id
     $featured_id = $this->db->select('video_id')
               ->from('table_name')
               ->where('current_featured_id',1)
               ->get()->row()->video_id;

     $new_featured_id = $featured_id+1;

     $update_featured = array(
         array(
              'video_id' => $featured_id,
              'current_featured_id' => 0
         ),
         array(
              'video_id' => $new_featured_id,
              'current_featured_id' => 1
         ),
     );

     //update your db
     $this->db->update_batch('table_name', $update_featured, 'video_id');
}