For free domains Cloudflare is a strict requirement -- because SSL is required, and the reverse proxying (orange cloud mode) by Cloudflare is able to provide the SSL on your domain.
Without this, SSL will not work and your domain will be non-functional.
We do have a Premium Domain offering which is now in beta -- contact us for more info. There will be a nominal charge of $5/mo per premium domain, but you can then use any DNS provider.