Your Stitcher downloads will appear in your hosting provider's stats. 
For more in depth listening metrics and insight to Stitcher listening, you should also check the Stitcher Partner Portal regularly.

You can login to your partner portal using the email you provided with your show submission at the below link.

https://partners.stitcher.com/

If you are unable to log in to the Partner Portal, check out this FAQ or email Content@Stitcher.com for assistance.