Hi there @TheSuburbs,
If the gift card codes are already created, you could upload them into Klaviyo as custom properties for each profile and use the 'person | lookup' tag to pull in the value for that property in your email: Template Tags and Variable Syntax
However, I'm afraid at this time that Klaviyo does not have any native support specific to Shopify Gift Cards.
As a workaround, I was able to find that we do offer an existing template for sending a Gift Card Notification. You can see that when reviewing the Shopify Notification Templates here:
You can use that template as a starting point for how you want to email to look. You can then also replace any of the variables in the email if needed. You can then export the template HTML for use in Shopify.
Hope that helped,
Alex