Without jailbreaking, I don't think you do. You can do it at the router level with dnsmasq, but then you'd always have to be VPN-ed into that network when you are out and about.
Although, I believe Cloudflare DNS app on iphone uses a VPN iOS API to do it's thing, so it should be possible to put dnsmasq-like functionality into an iOS app. I don't know if this exists already.