My recommendation is, before changing nameservers to Cloudflare ones or vice-versa, replace the value 10800 (180 minutes) with 300 (5 minutes) for your DNS records at your current provider (via cPanel or some other interface if it allows you)
Moreover, the DNS nameserver propagation for a domain usually is up to 24 hours. Depending on the TLDs as far as I have tested, some have 1 hour “update rule” so they check after an hour of your changes and gather new information, while for others like ISPs at my country I have to wait 24 hours.
You can prepare, change the TTL value to lower one for today, and consider doing the nameserver change for a few hours later or even a day later (tomorrow) in the time when the Website traffic is as lowest possible to make sure there would be no interruptions.
In case, you can flush the needed DNS records for your domain using the tools from the list below:
I recommend to add A record instad of CNAME for forum, portal, www, webmail, secure sub-domains and point them to IP address just like for @ A record and make sure to have them (proxied via Cloudflare).
Regarding E-mail service, the A mail record make sure it is (DNS Only).
Also, to note consider adding an MX record for yourdomain.com which points to mail.yourdomain.com (the A mail record which should be to make the email working).