AzuraCast has got some web proxy option regarding Cloudflare, so it can proxy over HTTPS connection and 443 port using Let’s Encrypt SSL (docker setup), and you benefit from Cloudflare Full SSL (Strict) option too.
Until then, I am afraid I cannot provide any other helpful information and even do not know about this feature too.
NOTE: Check this post due to Terms of Usage - I am not sure if this is related to what you want to achieve and the above example using AzuraCast and Cloudflare: