While Cloudflare does offer the means to update DNS records via API, they do not offer their own domains for DDNS use. If moving a domain to Cloudflare isn’t going to work for you, you will need to resort to a third-party solution or roll your own with your existing DNS service.
Recommending a third-party DDNS service is out of scope in the Cloudflare Community where the discussion topics are intended to focus on services that Cloudflare provides. Fortunately, there is an ample supply of articles on this topic that will offer the resources you are seeking.