Smart Notifications add-on is using Atlassian Connect API to communicate with your Jira Cloud instance. It does so on behalf of current logged in user. Communicating with Slack is carried out via Slack API using OAuth authentication. We do not store any information taken out from either Jira or Slack externally on our backend except for user's access token and information about assigned channels.
"Access token" is required to access Slack API on behalf of the user and we receive it during the "Connect with Slack" procedure. Once connected, add-on will be able to send notifications to selected Slack channels. Any user can revoke their Slack access token at any time, using this link. Unfortunately, this can't be done directly from Jira as the Slack API does not provide such feature at the moment.