Privy needs to talk to Mailchimp in general first via a signup integration before the signup codes it generates can be pushed and stored inside Mailchimp and thus accessed by Mailchimp newslettters/automations. Something like this: https://help.privy.com/hc/en-us/articles/360009564293-Syncing-Your-Privy-Contacts-To-MailChimp
You'll need to make sure you created a custom merge field inside Mailchimp to hold the values of the signup codes. To do so, you'll need to go to Audiences > Settings > Audience fields and *|MERGE|* tags. Make sure you have the right Current Audience selected:
Then you can go Add a Field (type text) and name it something like this:
Don't forget to Save Changes.
Afterwards, you'll want to map your Privy coupon code field into that Mailchimp custom field you just created. This documentation should help: https://help.privy.com/hc/en-us/articles/360007991614
Once that's done, you can call that custom field into your emails using Mailchimp's merge field syntax, i.e. as in the example *|SIGNUPCOUP|* or *|MERGE6|*.
Hope this helps!