Fuzion tokens for membership start and end date
The issue is that a contact can have multiple memberships, so you can't use membership tokens unless you display your search results as memberships.

In Advanced Search, do your search again, but change Display Results As from Contacts to Memberships.  If your contacts only have one membership each, this is all you need to do; if they can have multiple memberships, you probably need to filter by date, membership type, or status to get the correct ones.

From the search action selector, you'll now have the option Print/merge document for membership.  When you select that, the list of tokens will include membership start and end dates.

UPDATE: I've posted a video here demonstrating what I believe is the answer to the question: https://www.youtube.com/watch?v=5D2aLoW9ovU&amp;feature=youtu.be