If website is pointed with A record to web host instead of name server how does this change the process of routing the site through here?
You can’t use Cloudflare IP addresses as an A record. You’d need to use Cloudflare Name servers.
In many cases my clients will have registered the domain name with godaddy, they point their mail to microsoft 360 or gmail with an MX record… then point website with A record.
How can I make this work for those situations? because if I change the name servers it will mess up the mail.
Cloudflare DNS should have all the same DNS records as their current host, including mail hostnames. That’s the right way to do it. Here’s an article on configuring DNS for mail: