Slack requires an enterprise plan to invite individuals via API but you can still use Headcount to send invites for Slack using the manual Slack invite option.
Simply navigate to your Slack members page under Administration -> Manage Members.
Then select Invite People.
Once you've copied the invite link copy it into your Headcount account.
Once you've added your link, click Update and then you can invite contractors to apps you use.
Make sure you only add the invite link and not any of the extra text added.