Using the "vine" BBCode and the URL to your vine, you can embed them in your post.
Example:
Vine URL:
Attachment 1633
Then embed using "vine" BBcode:
Attachment 1634
Result:
Note: The embed doesn't come through on TapaTalk as they don't have access to the vBulletin translation. I'm working to have it translate the BBCode to display you with the URL when browsing the forum using TapaTalk.