The internet suggests that the official desktop/web client is not particularly usable with a screen reader:

https://www.marcozehe.de/2016/01/16/status-of-the-accessibil...

https://slackhq.com/designing-slack-for-everyone-456002920bf... (talks mostly about the mobile clients, which were designed later)

Maybe this has changed recently?

It's closed source and not ported to all operating systems that people might use.