Moving Domains to Cloudflare with 0 downtime

Hey, so I have very little experience with DNS, Google recently moved me to Squarespace and they're charging me fees. I have a few domains I want to move over, but I cannot afford any downtime on my email forwarding, Squarespace provides free email forwarding to my gmail, which uses these MX records. My first issue is, Cloudflare needs to be configured to forward my emails as I'm guessing Mailgun will no longer work after I leave, and secondly, I need to transfer the domain without emails going missing. My thought was to use cloudflare's MX records on Squarespace before the transfer meaning I don't have to switch them after Mailgun gets disabled, but I'm not sure what's best. Thanks!