GTA Online has a fair share of armoured vehicles but they are rare and well-hidden, sometimes in plain sight, in the singleplayer version of GTA V.
Rockstar Games create game worlds that are massive in scale at the time of release but by no means barren of content. In fact, they are some of the most detailed worlds in the industry and they often hide amusing and even useful secrets. One of them is Duke O'Death, that many players don't know exists in single-player even to this day.
Who can get Duke in GTA V singleplayer
Unfortunately, the reason for many not knowing about the car is that not everyone can get it. Only players who had a Rockstar Social Club account while playing GTA V on Xbox 360 or PlayStation 3 and then obtained the game on Xbox One or PlayStation 4 can trigger the prerequisites for the Duke.
How to get the Duke in singleplayer if I didn't and don't have a PS3/Xbox 360
You have a few different options here. One is to find someone with a PS3/Xbox 360 that is clean and have them unlock the limited content for you, regardless of your current platform. If you want to know more about this method of unlocking content, you can see the example of Classique , a member of GTA Forums who is running this service at no cost.
Alternatively, PC players basically have no limit to what they can mod into their game, Duke included. Modding singleplayer is not illegal, doing it in multiplayer will get you in trouble.
How to get the Duke in GTA V singleplayer
If you satisfy the requirements above, you will need to complete the Pulling Favors mission that introduces you to Strangers and Freaks. For reference, that's the first mission for Tonya where Franklin helps her out with towing vehicles.
After that, you can go to a gas station in the Sandy Shores area that will have a Duke O'Death in its parking lot. You can find the exact location in the image below.
Enter the Duke and five hostile NPCs will spawn in various vehicles. Two of them will be driving Phantom trucks and three will be driving SUVs. You can either kill or outrun them to complete the random event.
After event completion, you will be able to find Duke O'Death parked in Grand Senora Desert or El Burro Heights. More directly, you can purchase the car from Warstock Cache and Carry but by far the best and easiest way to get it is to just pick up your phone and call 1-999-33284227.
If you are having a hard time memorising the number, just remember that 1-999 is used for all phone cheats in GTA V while the rest spells out the name of the cheat. It's "Deathcar" in this case and one press of a number corresponds to any of the three letters below it. For example, number three has D-E-F beneath it so if you start typing "Deathcar", the first two letters will be typed as "3-3", letter A will be number two and so on.