Unfortunately, Instagram does not provide a solution to use Instagram DM via 3rd party integrations. We are looking into a workaround for this, though.
Integrating your Instagram account(s) into Zendesk still allows you to track, reply, set up automation, and get statistics on your Instagram activities - in the same place you have all your other customer interactions.
This is why we're sure you'll like it. Give it a try, the first 14 days are on us 😃