How can I use a custom DNS server on my schools network?

They seem to block any DNS that isn't their own. I've tried 8.8.8.8 and the new cloudflare one. Both blocked, it's a real issue because their default dns dies for about a minute every 12/24 hrs causing my VPN to go down.

How do they even block external DNS servers?

one option would be a local dns cache like dnsmasq, if they block outgoing connections on port 53 which they most likely are that would be your best option. other than that switching your vpn to tcp might make it better since keep alive might allow you to bypass the dns lookups

They can block udp 53 to anything they want, or may be blocking all traffic to known fins from a list or something

Look into dns over https or dns over tls. Good luck blocking that

DNS caching might be the best option available.

I've already got my VPN over tcp, when I had udp it would drop out every few minutes (idk why). Switching to tcp keeps me up for a few hours and then DNS resolution fails to the privateinternetaccess.com (my provider) causing it to go down till I restart.

I like the idea of DNS over https but I think that's application specific right, they have to support that?

I'll look into dnsmasq, never used anything like it before, caching is new to me