Privacy works similarly to Gmail. It is NOT encrypted end to end like some secure messengers are, but messages will never be shared with any Imgflip users or moderators except who you explicitly specify. Right now that's just who you're chatting with but it could include moderators in the future if we added a "report this message" button or something (otherwise there would be no one to report to).
Queries can always be run on the database for the purpose of improving the engineering of the system, but this access would only be given to veteran engineers, and is currently limited to just one engineer.