At this time, any user with Browse Project permissions is able to integrate JIRA with Slack. This can cause problems where non-JIRA users are part of the Slack channel and should not see updates from JIRA.

As a JIRA admin there's no easy way to disable all users from being able to integrate JIRA with Slack. A permission scheme for Slack integration is currently being requested where JIRA admins can determine which users can integrate JIRA with Slack and which users can't. The ability to disable JIRA integration entirely is also functionality that is desired.