Sometimes I want to know if a specific person has seen a message yet without having to Direct Message them. Is it possible to see read-status in Slack? How?
Unfortunately there is no read receipt feature, although it is on their dev backlog according to this Tweet thread.
There isn't much you can do outside of asking if they saw it. Some other possibilities:
Look at their screen to see if their Slack app is showing the unread message notification. This isn't perfect though. You'll know they read it if the notification isn't there, but they may have also seen it even with the notification showing, due to other unread messages.
If they are offline when you message them, wait around to see if they appear online shortly after you send the message. That is a likely indication that they read it. Having said that, it might be possible that a user's account is "sleeping" and the act of receiving the message sets them as online. You can test this with someone that has the Slack app on their phone. Have them login and leave the app alone for some time. Once they no longer appear online, send them a message and see of they come online without having to reopen the app.