Start it, and get an email when it's ready
Under Export data, pick public channels or all channels and direct messages, then messages from the beginning, the last 12 months or the last 90 days. Leave Include files on to add the photos, documents and call recordings shared there; files over 1 GB are listed but left out. Start it and close the page: the export runs in the background, the list shows how far it got, and Freesbe emails you when it's ready. One export runs at a time, one a day.

