Concerns after linking my custom domain through a CNAME Record, and using Cloudflare's nameservers

It shows a cross next to the settings because your domain is using Cloudflare’s nameservers instead of ours, and is pointing to Cloudflare’s IP addresses instead of your website IP with us.

Like the text in the screenshot says: this is fine if Cloudflare is setup correctly, but our DNS checker has no way to tell. So you’ll have to check it yourself.

Besides that, just ignore the crosses. It’s not recommended but it’s also not broken if it works for you.