Peanut
3
Thanks @alzhao 
The config was as follows:
[Interface]
Address = 192.168.3.3/32
PrivateKey = <PRIVATE_KEY>
DNS = 192.168.1.1
[Peer]
PublicKey = <PUBLIC_KEY>
AllowedIPs = 0.0.0.0/0,::/0
Endpoint = <ENDPOINT_IP>:<ENDPOINT_PORT>
PersistentKeepalive = 25
I changed the DNS to 1.1.1.1 and it allowed me to maintain my connection when the kill switch was enabled. 
The endpoint router is configured to use NextDNS and I would like to be able to use this over the VPN connection too, do you know how I can do this?