On a free Slack, can an owner/admin view private channels?
According to @SlackHQ (the official Slack twitter account), "owners can only see the private channels that they are a member of".
As of May 2019 Slack's privacy FAQ states that on a free plan, owners can request an export of all data, including private messages and channels. However, they must "provide (a) valid legal process, (b) consent of members, or (c) a requirement or right under applicable laws."
There is workaround though. If you have a Slack app that collects tokens from all you users, that app is able to access all private channels.