Certain DNS server have policy to log and store user data either temporarily or forever. So while usually there's no security risk (unless you choose to use rouge/malicious server), you need to consider the privacy problem. CloudFlare and Google DNS would be bad choice if you have serious privacy concern.
The last is, how possible of leaking your recovery seed through the DNS server? Never heard of this but gotta be very careful.
This should be impossible, unless your wallet software is stupid enough to send recovery send to DNS server.