I'm not familiar with the project. Does it use any net-related code? That won't be static because it will want to load C-libs for using /etc/nsswitch.conf to handle DNS/name stuff.
I don't have the source code in a good state to publish yet but here's where I'm at. At some point before this CGO_LDFLAGS does work and the header is found (omit the -ldflags args). But when it goes to statically link it can no longer find the header.
CGO_LDFLAGS="-L$(pwd)/duckdb/src/include" CGO_CFLAGS="-I$(pwd)/duckdb/src/include" go build -ldflags '-extldflags " -lstdc++ -lm -lduckdb -static"'
# github.com/marcboeker/go-duckdb
../../go/pkg/mod/github.com/marcboeker/go-duckdb@v0.0.0-20220427142532-cd9f33e64d9a/connection.go:4:10: fatal error: duckdb.h: No such file or directory
4 | #include <duckdb.h>
| ^~~~~~~~~~
compilation terminated.