Before I get into specifics let's first take a look at what Van Dyke Brown is on a fundamental level. There are quite a few manufacturers that actually consider Van Dyke Brown as a black instead of a brown, Why? Because the modern variants are mixed colors based on a black pigment.
Take a look at your tube (or tubes) of Van Dyke Brown. Chances are that on the back you'll notice two pigments listed. The most common you'll find are PBk9 and PBr7, while others include various combinations of Pbk11, PR101, and NBr8. Some even include a yellow pigment such as PY42 or something similar. Most of the time, however, you'll find the PBk9/PBr7 combination.
The order in which the pigments are listed usually indicates the relative amount of each one in the tube, as if they were ingredients you would find on the packaging of just about anything at a grocery store. The fact that there are two or more pigments listed indicates a mixed color, which Van Dyke Brown usually is. There are exceptions, of course. Generally speaking, there is a bit more black than the other pigments.
Let's take a look at the PBk9 and PBr7 pigments:
PBk9 is an abbreviation. It means "Pigment Black 9". PBk-9 is the pigment commonly known in paint lingo as Ivory Black, and it typically comes from the ashes of charred bone.
PBr7 is also an abbreviation. This one means "Pigment Brown 7" - it is an earth pigment composed mainly of natural iron oxides. You can find this pigment all over the place, as it is commonly used for colors such as Raw Sienna, Burnt Sienna, Raw Umber, Burnt Umber, and several other mixed colors.
Earth pigments like PBr7 cause oil paint to dry more rapidly than any other pigment... something to be aware of if you find your paint drying out too quickly. Anything with PBr7 mixed into it will oxidize at an expedited rate based on the amount that has been introduced.
What this means to us as painters is, essentially, that we can make our own Van Dyke Brown by combining some amount of Ivory Black with a smaller amount of Burnt Umber or Raw Umber. These are the darker browns and are best suited for the Van Dyke Brown mixture. Start with 3 parts Ivory Black to two parts Burnt Umber (or Raw Umber) and see where that gets you. Depending on the brand of paint you are using, you may need to shift the ratio slightly one way or the other.
Note that your choice of the two umbers will determine the mixture's temperature bias. The difference will be subtle, but you can play with it. Raw Umber will create a cooler variant with a slightly greenish hue, while Burnt Umber is warmer and will impart a reddish hue in comparison. Combine both umbers for something in-between.