Here's the code: https://github.com/mattermost/platform
From the look of the screenshots ( http://www.mattermost.org/70-2/ ), I'd say there are some copyright concerns with the styles. This isn't a Slack alternative, it's a Slack clone. That's very problematic from a copyright stance. Why not create your own design style?
Gogs had (has?) this same issue: https://github.com/gogits/gogs/issues/1069