How do I set up Slack to send notifications to my Android phone?
You might have different settings for each channel, so that the channel you are testing with, does not send mobile notifications. 

With a channel selected in the sidebar, click the Notifications icon (the bell), and check the settings for the channel you are viewing: 



In the Mobile push notifications section, make sure you have not selected Nothing. And make sure you have not checked the Mute this channel option: