You can configure the DHCP server on your Flint to give DNS to client devices to be your AdGuardHome site via LuCI → Network → Interfaces → LAN → Edit → DHCP Server → Advanced Settings → DHCP-Options. Enter the following and click Save, then click Save & Apply:
6,20.x.x.x
where 20.x.x.x is the IP address of your AdGuardHome site
I did this also in my tests. I think the Custom DNS Server setting in the GL.iNet UI works differently, on the router’s dnsmasq, and does not send the DNS to client devices.
EDIT:
On my own network, I have the main router set up to give DNS to client devices, which is AdGuardHome running on a separate NAS server on the same LAN. I do not use dnsmasq on the main router.
I do not work for and I do not have formal association with GL.iNet