There is no official Slack app for BlackBerry 10. Also, if we open a slack channel on the native BlackBerry 10 browser, it just takes to the team settings page. I have figured ways to make it work though, which in fact is quite simple. Quick way is to enable desktop mode in the BB10 browser and then channels load instead of seeing the settings page for the team. But it's not at all user friendly and unsupported browser message will be shown.
Another way is to install the Slack app for Android by sideloading the apk file. This works fine when the team uses email for login. But, when it's configured for SSO only, then we have to follow additional steps. The native browser can open apps that have deep linking registered. Slack does not seem to have this. In order to make this work, we need to use a browser which also runs on the Android runtime. So get the Aurora Browser installed, open the Slack app, choose SSO sign in and this time choose Aurora browser when the dialog pops up. After authentication, a page will be shown with a Download Slack app or Open in Slack app buttons. Choose the later and the Slack app launches, and you get logged in to the team. Enjoy all the awesomeness of the Android Slack app.
I have not checked whether notifications will get received. But I doubt that. So if you don't receive it, you can choose the send email notifications when away for five minutes option from the team settings. Though there is a slight delay in you getting notified, the problem is solved.
I have tried S10 app from BlackBerry World, but for some reasons, I don't get any notifications. Plus the app is rather minimal with text only interface. Kind of have an IRC feel to it.