You can, but due to a current limitation in the Apple's sharing API, you can only post videos to Google's YouTube from within the YouTube App itself (not directly from within Brivvio). The same applies for posting videos to Vimeo. It's on our roadmap to develop a way for you to share directly to YouTube and Vimeo, but in the meantime here's an easy workaround...
To post your video to Youtube (or Vimeo), just save your Brivvio video to the Photo Gallery on your phone, and then open either the YouTube or Vimeo App and post your video to your YouTube/Vimeo Channel by selecting it from your phone's Photo Gallery.
Jargon buster: API means Application Programming Interface - it's what let's different apps talk to each other.