Luffy uses Conqueror's Haki in Episode 473 ("The Warlord's Seal Broken!") during the Marineford Arc.
You will not see Luffy consciously use Conqueror's Haki again until much later (the Post-War Arc/Return to Sabaody), but this Marineford moment is his first major, visible display of it. which episode does luffy use conqueror's haki in marineford