Anyone with the "manager" or "account owner" permission can delete messages sent by themselves or by others. Team members can not delete messages
From the mobile app:
Long press on the message and select "Delete Message"
From the desktop:
Click on the three dots icon next to the message, and select "Delete"

You can see messages even after they've been deleted. You can do this by logging into your account on breakroomapp.com on a computer. From there, find your deleted message, click on the "eye" icon and select "View original message'

Breakroom Chat as a Crew App Alternative
Breakroom Chat as a Slack Alternative
Breakroom Chat as a When I Work Alternative
Breakroom Chat as a Homebase Alternative
Breakroom Chat as a Microsoft Teams Alternative