I pointed the dns name servers to infinityfree.net (ns1.epizy.com and ns2.epizy.com). I need to add my domain to cloudflare as infinityfree does not provide dns altering for free hosting. To add to cloudflare, nameservers has to be pointed to cloudflare. If I do so, does my current site stop functioning because of the nameserver change?
If you want to use Cloudflare you need to copy all of your DNS records over to Cloudflare or use their automatic import tool. Then you need to go to your domain registrar's account portal and set the nameservers to the ones that Cloudflare tells you to use. As long as the DNS records were copied over correctly the website will continue to work without issue, just using a different name server.