If slack being down means you lose all insight into your build process and code management, you seriously need to introduce a secondary option immediately.
OP didn't say "all insight". There's a difference between being unable to see a stream of change events and not being able to see the current state of the system. The latter is completely unacceptable, whereas the former is just annoying.
I'm sure they have fallbacks, but when their ecosystem (apparently) evolved around Slack, the fallbacks are less effective. Polling Jenkins to see when your job is done is more time consuming than receiving a Slack message.