I found the LEGO set High Speed Chase, and it says that "Includes unique code to unlock special missions and vehicles in the LEGO City Undercover video game." What missions and vehicles, and are they available by other means?
Take a look here for a look into the LEGO City Undercover code releases
From what I found, the content in the pack unlocks 2 police car chases (for missions)
TL;DR If you are strictly looking for in-game content see below, otherwise I have been able to find a purchasable DLC code ONLY in the lego set as described in the OP:
If you take this LEGO game survey you should be rewarded with a key to unlock content.
I also found these that might work (haven't tested them yet) via here:
mhhrhm: Race car driver
xkgzvj: Gorilla suit guy
hvgtpg: Natalia Kowalski
N7NN4F9: High Speed Chase Missions & Vehicles Unlock Cheat
3GCC7XR: Justice & Red Sports Car Unlock Cheat
Here is a video confirming the reddit post.