Reverse Proxy for External URLs

Hello,

In my website, in order to protect our users’ privacy, we use a “proxy” for any images that are external to our domain.
When a user creates a post with an image that is not hosted on my website, we will transform the URL of that image to use our own “proxy”, which will download the image, cache it, and display to the viewers.

One of the main reasons for this is to avoid users finding the country/IP of another user, through a “fake” image, that executes a script.

Is this kind of functionality existent in Cloudflare that I could take advantage of?
I understand I can have the basic caching functionality of Cloudflare against my “proxy server”, but I wonder if Cloudflare has this functionality so that I don’t have to use my server at all.

Thank you very much.