Anyone should be able to get this done in under half an hour.
-Start up a new game of Breakdown (preferably on the lowest difficulty, higher difficulties tend to spawn you further from cars)
-Do your best to sprint to the road, then sprint to the closest car or building in hopes a car is near by
-Shortly before or after you get the car you'll get the audio of your character and Lily talking
-Find the closes "?" on the map to establish your base
-Pull all three Molotov's out of the base inventory
-Not drive around honking your horn to find clusters of zombie
-Kite/sheep herd the zombies in to a cluster, chuck a Molotov
-More zombies will probably be running over to you, rinse and repeat the last step or jump in your car and find another cluster
-Once all three are used, quit out and start this process all over again
I personally have no idea how the Molotov works, I just press the throw button and hope for the best.
Sometimes you won't get a lot of zombies, don't worry about it. Just keep repeating the above and you should get it done all the same.
If you have Zeika Rivera unlocked, select her as your character as she starts with Chemical Incendiary. If you don't have her though then don't waste your time getting her. You won't be saving much time considering how quickly it can already be done without her.
If you have access to the special Incendiary Revolver through the radio, get that. It only has three shots but it counts as a shotgun so it has a wide spread and the benefit of counting for this achievement:
I found out Andy Pimms is another great character for this if you already have them unlocked, starts with a lot of Chemical Incendiary's just like Zeika. If you don't have him though, just stick to the method of playing as whoever and just setting up the base, getting the three 'tovs and then restarting once they're used.