Digify lets you share files privately and self-destructably

Shared files can't be forwarded, downloaded, or copied by their recipient. There's even protection against screen-copy attempts. 

Shared files destroy themselves after a time limit between one minute to one month, and in the meantime, you have the ability to un-share them at any moment.

For the time being, Digify is a free app, and its developers are on the lookout for feature requests and bug reports, so if you are interested, now is the right time to jump in and contribute to it becoming an even better experience.