What's this style called? What's the best way to emulate

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Adobe Illustrator Tracing.

vector art prolly

>>3082541
Pretty much.

http://www.designfreebies.org/design-tutorials/vector-tutorials/10-outstanding-vector-portrait-tutorials-using-adobe-illustrator/

It's more of a technique than a style.

Illustrations like these are often made with the intent of being screen printed (even if they never are). That means they need to have limited color schemes, and gradients need to be carefully used (if used at all).

Tracing is often used, but in order to do it well, you still need to know your shit.

>>3082365
The effect is called "posterization", a common vector art practice. Let's call it a comic-styled vectorization. There you go.