If you want to get such a domain, you can sign up for JIRA OnDemand where your going to have this kind of domain: https:\\[jira_instance].atlassian.net but this is not necessary to integrate with Zendesk, indeed your can integrate with Zendesk using any domain if your own.
To start with that, you may need to have Zendesk connector for JIRA (https://marketplace.atlassian.com/plugins/net.customware.plugins.connector.zendesk.zendesk-connector-plugin) installed in your instance and an active Zendesk instance.
For the full instructions, you can follow the details here:
Hope it helps!
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