Hi @Charzain,

Welcome and thanks for posting your question to the Community!

At this time, Klaviyo does not keep track of your customers that leave reviews on your website.  So if a customer receives your product review flow (requesting a review) and clicks through to your website to leave a review, Klaviyo knows that the customer received the email, opened and clicked through to your website.  However, Klaviyo cannot track whether or not the customer actually left a review for that product.  
Because of this, if you want to create a follow-up flow to send a coupon to your customers who do leave a review, you will need to tag these customers in one manner or another.  The first option would be to manually add these profiles to a List and use a list-triggered flow to send your coupon.  The second option is to add a custom profile property to a profile after someone leaves a review, create a segment of customers with this property on their profile and use a segment-triggered flow to send your coupon.  The only downfall to this path is that profiles can only go through list/segment triggered flows one time.  
If you want customers to be able to receive the flow message each time they leave a new review, you would need to create a Custom API Event Call that is triggered each time a customer leaves a review on your website.  This event would send over to Klaviyo and you can use that event (and event data) to trigger a flow message containing a coupon.  At this time, Klaviyo support cannot assist with creating/maintaining Custom API Event calls beyond providing our API Documentation: 
Klaviyo API Documentation
Klaviyo API Reference Guide

In order to trigger a flow to send an email when a review is submitted, Klaviyo would need to receive that as an event.  You or the review platform you're using would have to create a script to send that data to our Track API.
You can also create a conditional split based on those who have clicked the product review email in the split. However, you will need to send at least one of these emails before that option populates in the dropdown. The condition would look like What someone has done > clicked email at least once over all time where Flow equals product review cross sell.
If you want this email to only send to those who have actually completed the review, you can work wit a developer to use our Track API to create a custom event for a product review, and split based on those who have done a review. This would also create a custom property (such as "Submitted Review") you could trigger an flow off of, and send the coupon that way.

Using a third party app or plugin for your store integration will definitely be the easiest in terms of saving that data to a database, adding it to your site, syncing those reviews to Klaviyo and handling the forms.  Our most popular integrations are Yotpo and Stamped.io:

https://www.yotpo.com/integrations/woocommerce/
https://help.stamped.io/article/8-getting-started---woocommerce-wordpress

Customers are a big fan of Yotpo because they allow you to add the reviews to emails very easily, send segmented emails based on specific responses collected (trigger flows) and also has a pretty easy setup.  I'd check those two out.

A custom integration would honestly be pretty complex and would really depend on how you want to store the data outside of Klaviyo.  You'd need to collect the reviews with a Klaviyo form as a custom property, set up a cron job to pull that data regularly via the API and all of the review on site stuff would be up to your dev team.

Hope this helped get you in the right direction!

Alex

Thank you Alex.

Very detailed answer.

I'll try your suggestions out.

No problem @Charzain! Let me know how you end up setting up the flow :)