From what I can tell, it seems like Reddit has a whitelist of oEmbed providers, and that list only includes the big, trusted sites like YouTube. You could try enabling “Change oEmbed to video instead of WordPress default photo/excerpt” on the Videopack settings page in the General tab, Plugin Settings / Video sharing. Open Graph tags might be used to embed a video in some cases. You can turn on “Enable Facebook Open Graph video tags” and see if that does anything.
Either way you’d post a link to a video that has a Videopack video embedded in it, and see what happens.