Keep track of important conversations; pin, save or star
Create a culture where people cc you if they would like you to address the message. You can ignore ones you're not tagged or not addressed to @here or @channel
How?
Think how you write emails; subject line, message body, the addressee (cc)
Introduce each topic you post as a new message. Use the topic as the subject. Conversations and responses around that topic should happen in a thread
CC anyone else you need to need pay special attention to the message