Are the records proxied? If not, the process is down to the browser which will receive all the IP addresses that resolve in the DNS and then try them in whatever way it does.
If they are proxied, round-robin DNS doesn’t do any healthchecks so Cloudflare can’t know which connections are up. It will try one (that then seems quite sticky to prevent issues with sessions I assume, I’m not sure of details about how that is done or how long for), then try another.
How long that takes depends on how the server is “down”. If the request traffic is dropped somewhere, then you need to wait for the connection attempt to timeout. If the site is reported as unreachable, actively rejects connections or has an SSL problem, the retry will happen very soon. States that would return Cloudflare 521, 522, 523, 525 or 526 error codes trigger a retry.