It does however require support from your hosting provider as well, so that Cloudflare is able to download the zone file from their name servers.
If you’re actually looking for the kind of redundancy that mixing different and independent providers may be able to provide, then it doesn’t make sense to take 7 name servers from one provider, 7 from a second provider, and 7 from a third provider (and thereby have a total of 21 name servers).
What would make sense in a such set up, would be to have three name servers - one from each of these three independent organisation, given this specific example mentioning three providers.