Many DNS providers have the ability to do AXFR "zone transfers", so you can sync your records to a secondary provider and you would add a secondary set of nameservers for redundancy. Unfortunately Cloudflare doesn't offer this unless you pay for their Enterprise plan (they started offering it earlier this year).
I do love using CloudFlare for DNS, lots of great features and generally works well, but I wish they would support AXFR for the lower tiers. I've been working on a solution for this using the CloudFlare API, but we'll see how well it works out.
Back in the day (I haven't run my own mail server for years and years) there was a company called Secondary MX.
That's all they did. They weren't a mail host or provider, there was no UI, nothing. All they did was allow you to specify them as, well, a secondary MX, so if you were offline they'd cache your inbound email until you were back. Simple. Efficient.
I think they want to price discriminate: the costs from AXFR should be minimal, as it is an old technology, very optimized and low bandwidth.
However, cloudflare decision turns cloudflare "free" offering into a free SPOF. They should extend this offer to their free users, who could then use the secondary DNS that most hosts/domain name sellers provide for free to the IP that is proxified by cloudflare. It could even be limited to the case of proxy or cloudflare DNS failure, so that cloudflare could still price discriminate (make AXFR fail, unless cloudflare is down, like a dead man's switch)
Fwiw, you could use stack overflow DNS Control to manage your DNS records and upload them to many providers. Then the only thing you'd have to do is flip a line of code to fallback to the other DNS provider.
Amazing that this isn't "free" and folks have to resort to syncing records across DNS providers with proprietary, vendor-specific APIs. AXFR is standard. It's not just Cloudflare... AWS and Azure don't support it either.
I do love using CloudFlare for DNS, lots of great features and generally works well, but I wish they would support AXFR for the lower tiers. I've been working on a solution for this using the CloudFlare API, but we'll see how well it works out.