Setup a new flow and used my private email to test but didn't receive any email?

Welcome to the community @Oriusu 

From what you’ve shared, the flow looks OK. However, things to check if you haven’t already.

In your test email profile:

• do you see a checkout started event? If not, is the filter you have on the trigger preventing you from entering? You can check that by previewing the trigger and searching for your test email.
• Are you seeing checkout-started events for other profiles in https://www.klaviyo.com/analytics/metrics ?
• Is the checkout email showing as ‘received’? If yes, did you check your spam folder?
• Is your test profile ‘suppressed’ or ‘unsubscribed’? If either of those, Klaviyo won’t send the email.

Hope that helps

Andy