Slack users can apply for a leave right from the Home Tab of Remoty's Slack Application.
Click on apply for a leave and you can then select from the possible leave type from the option as shown here:
Hit the Request button in the bottom right corner of the dialogue box. Your manager will receive your leave request, along with notes and other details.
You will be notified by Remoty in DM when the user (whom you have requested) accepts or rejects your leave request.