No. Once a name is resolved to an IP - that IP is used for that domain. For the HTML on the site Cloudflare is protecting there's no way to redirect a user.
However, you can host your content (images, videos, js, css, etc.) on a different CDN with a new domain. This would trigger a new DNS request.
The problem with this is that people can still attack your servers. Anything that exposes the IP address of one of your servers will mean they can attack it. This defeats the point of Cloudflare.
The other point I have to raise is that if you're using Cloudflare - it's already acting as a CDN. Depending on your purpose, you could be building a redundant system.