What you could do is move the nameservers to Cloudflare. In that case you shouldnt have any nameserver propagation issues should you eventually switch to another host or even stay with Godaddy (God forbid 
). In this case you could initially use Cloudflare only as DNS provider (
only) and try to fix the 521 issues.
Should you switch to another provider you’d only need to change the DNS records on Cloudflare and Cloudflare typically propagates these changes relatively quickly, though other resolvers still might cache it. Should you use Cloudflare as proxy however (
) there wouldnt be any propagation issues and a change in IP address would be pretty much instantaneous.
Now as to why you get a 521, that is difficult to say but there is a good chance Godaddy might be (as mentioned earlier) rate limiting requests, in which case only they could fix that.