So I am trying to make my new website hosting safe with Cloudflare, the issue is the hosting I use needs these as the nameserver because otherwise, the subdomain feature I have will not work:
You can’t use other nameservers with CF - either one or the other needs to be the authority for your domain. If your provider doesn’t support another DNS provider being the authority, you either need to contact their support to see if they can do something custom, or switch providers. Most providers do just fine with you using different DNS as long as you manually add new subdomain records as needed.
Well technically… you can if you are an Enterprise customer and are using Cloudflare in Secondary DNS mode (makes it a challenge to take advantage of other potential Cloudflare features like WAF/CDN since the other DNS provider would be exposing your origin IPs and bypassing Cloudflare).
But not a terribly common scenario in my experience.