Julie here from Shopify Support.
It's great to hear that you're using Klaviyo for email marketing! This is a great way to communicate with your customers, share discount codes, and announce new product releases.
How are customers receiving the discount codes? Since they were generated in Klaviyo, it's safe to assume that you've added the discount codes to your emails. If that's the case, you'll just need to make sure that you're following Klaviyo's instructions on using dynamic coupons with Shopify. There, you'll learn how to ensure that your discount codes are added to your emails so that customers are easily able to apply them to their orders.
Keep in mind that since Klaviyo allows you to create discount codes, customers are responsible for entering the codes during the checkout process; unlike automatic discounts, discount codes are not automatically applied to orders. If you are noticing that they aren't being applied during the checkout process, then this likely indicates that your customers aren't entering them in the discount code field.
In this case, I recommend entering a message in your emails letting customers know that they'll need to enter the code in the checkout. This should help clear up any confusion with customers and you should notice an increase in usage.
However, if you're experiencing issues with the codes themselves, then I suggest reaching out to the Klaviyo developers directly. Since their app is responsible for generating the codes, they'll be able to help troubleshoot any issues with the codes themselves.
As you continue working on email marketing, I also thought I'd pass along our guide, "Learn Email Marketing: Everything from List Building to Advanced Lifecycle Automation". There, you'll learn all about the fundamentals of email marketing, the types of email marketing campaigns you can send, and how to track your email marketing performance. I think you'll find it quite useful.
I hope this helps, but let me know if you have any further questions!