Do Email DNS records have to be in Cloudfare?

Not sure which records you mean, but either way, no.

FYI:

  • MX records tell other entities on the Internet “these are the servers you contact to send mail to this domain”
  • TXT records are used for many purposes and the ones you’re talking about are likely either SPF or DKIM, both of which inform other entities “this is how you authenticate mail claiming to be from my domain”