Lazy (Plz don't shout at me because this is the unsecure way):
- https://www.guerrillamail.com/
- Cycle through these domains until you find one Slack accepts (If any)
- Make up a name you can remember, bearing in mind that this website does not use passwords and anyone can access your "email" address simply by typing in what you typed in. IE if I signed up for, say, twitter with the "mgkydigv" email you would be able to access that email simply by typing in "mgkydigv" for your name, and possibly reset the twitter account for it.
This method is great for literal throw-away stuff, it deletes emails within 1 hour of them entering the inbox.
Better:
That's why you should do what I did and make a not-a-throw-away-account on an email service you never use for your other emails and occasionally check in with it. Make sure to write down your username and super-secure password http://lmgtfy.com/?q=Secure+password+generator on a slip of paper, and possibly on a word/notepad document on your computer.