Your team wants to track SLA notifications in Slack. However, Time to SLA doesn't offer out of the box Slack integration right now (it'll be available soon).
We can use Time to SLA's notification mechanism and Script Runner's listeners to send SLA notifications to Slack.
Create a custom event to use in the SLA notifier so that other issue events don't get mixed up with SLA notifications. You can refer to Atlassian's documentation to create a custom event.
Configure a notifier for the SLA that you want to receive notifications about. You can also use your existing notifiers but the trick is that the custom event that you created in Step 1 needs to be selected in the Event section. Adjust the "notify before" and "recurring interval" sections according to your needs.
Follow Slack's guide to sending messages using Incoming Webhooks. You need to follow this guide up until and including Step 3.
Create a custom listener and use this code snippet from Adaptavist Library. You can modify the message as you wish.
Enjoy your SLA notifications in Slack.