When a coupon is first created in Klaviyo, the corresponding discount will not immediately appear in Shopify—it will only appear after a unique code for that coupon has been generated (i.e., only after a flow email sends out with a corresponding unique code in it).
Here, there are two unique objects:
Discount: This is the offer itself, defined by a set of rules
Discount Code: This is the unique code generated based on a defined discount
Klaviyo uses Shopify's Bulk Discounts API to create a single discount, and then multiple unique codes for that discount.
In the Shopify Discounts Admin page, you can search for the discount itself by the name you gave the coupon in Klaviyo. After finding this discount, you will see that it's tagged with "App" and there will be a summary of how many codes exist for that coupon and how many were used. If you click on the discount itself, you will see all of the corresponding codes that have been generated.
Please note that you will not be able to search for specific unique codes. This is due to a limitation on Shopify's end, but by searching for the discount name (as named in Klaviyo), you should be able to quickly find the discount and then click to find the codes.