There isn't any since it's not needed. The Windows DNS cache flushing thing is an ugly hack that's necessary because the Windows DNS client is an ugly hack. The Unix resolver libraries handle everything transparently. The closest you may come to ipconfig /flushdns is the situation where you run a caching-only nameserver and you need to restart it for some reason. Assuming it's ISC's BIND name server, it'd be
"Those who would give up essential liberty to purchase a little temporary safety deserve neither liberty nor safety."
-- attributed to Benjamin Franklin