The Slack app supports sending notifications to private channel. Select the private channel during the create new notification process and notifications will be routed to that channel.
Important: In order to send notifications to private channel, the Slack app must be added to the private channel separately. You can do this by going into the channel's info modal, then select "Integrations" tab. Click on "Add an App" button and add "JFrog Artifactory and Xray" app. This needs to be done on each and every private channels you wish the Slack app sends notifications to.