Click the little bell icon in the left margin near your name to shut yourself off completely, meaning whoever is trying to communicate with you via Slack will just have to wait. (inc.com)
Go to the Notification Center and select the crossed - out - bell icon on the bottom. (pocket-lint.com)
Toggling vibration still works the same, i.e. press the volume rocker then either drag the volume down to vibrate or simply press the little bell icon to toggle between sound and vibration modes. (androidheadlines.com)