Managed to get this after around 3 matches while also going for Pyro Prodigy using this strategy. I recommend running the Goo Gun, Pyro Grenade, RPG-7 and dome shield. I played Quick Cash as the games last longer and there ends up being a lot more instances multi team battles. Basically, you want to stick to the objective and goo gun the area around it. When you see an enemy nearby, light up the goo and put yourself in it and make chase with the flamethrower. You seem to stay alight for around 3-4 seconds so you don't have much time so I like to shoot a lot of goo around so all of it will light up giving you plenty of area to alight yourself. As a bonus, enemies nearby will take a good amount of damage. Use the RPG-7 when you have it, just make sure you are on fire first. The Pyro grenade is nice as you can throw it, run through it and shoot someone. The dome shield is nice to shoot through while you are taking damage from your own fire. You will die a lot but enough luck and you'll snag the 5 kills. Light players are your best bet as they die very quickly to the flamethrower even if they get away. If you see damaged players, throw the pyro at the ground to set yourself on and fire and try to finish them off.