Having acquired a new MBP, and being in the awkward position of not remembering each and every team I've logged in to on my current laptop, I need to somehow migrate teams across.
Since SO does not appear to have an answer for this yet (or a question). The answer is as follows:
On MacOS the file at ~/Library/Application Support/Slack/storage/slack-teams
contains JSON describing your teams. You can safely copy this JSON across to the same file on a new Slack install and your teams will be back.
You will still need to authenticate to each team, but that's a safe thing anyway. I assume the same can be done on Windows using the requisite file in %AppData%