I have recently started binge-watching the AMC show, "Into the Badlands", and I kind of want to take a class to learn that fighting style.
Daniel Wu studies Wushu so I am going to assume that this is the main art. In addition, executive producer Stephen Fung also serves as the series' action director alongside veteran Hong Kong choreographer, Ku Huen-chiu (reference). These imply a strong Kung Fu background.
I did watch the whole show and mostly it looks like generic Hong Kong marital arts mishmash. Therefore, I doubt that you will never be able to find just that style to learn as it is a style that was modified to look good on screen. However, looking in Wushu, and other forms of Kung Fu, you might find something quiet similar.
Just checked several trailers and fight scene videos, and as said in other answers, it's mostly flashy HK cinema fighting, based off of wushu. There's no clean style to be detected. However, there can be some influences from different styles detected.
The three monks battle: The "main" monk uses tiger claw. This is most often associated with Hung Ga, which also typically uses low horse stances and tends to avoid kicks, especially high ones. All these tend to return in how the "main" monk fights. The part where the three monks team up in a sort of triangle around the main character, attacking him with a sort of swinging arm punch, reminds me of pigua: big swings where the hit comes from minor hip movements and mostly from the shoulder, and the fist doesn't really matter.
The main character, Sunny, definitely uses wushu, but no specific style. I guess that fits his character well, as it doesn't limit him. It's what Bruce Lee means with "be like water" and "be formless".
The black eyed kid doesn't really do any style. From the videos I saw, he mostly seems like a kid who did a basic kickboxing bootcamp, but mostly relies on fancy effects and that open palm hit.
Haven't had time to check more videos, but if there're specific fight scenes you're interested in, I don't mind having a look. Mind you, there's so many styles of kung fu out there, I can only recognize some.
I started binge watching the show as well. It seems like different characters use different styles, and some of it is also blurred with movie style wire work. Sunny also uses different styles, but definitely see Wushu and Choy Lay Fut. The guy in the wheel chair used some Wing Chun techniques. It looked like in some other fights and training sessions, the different characters were practicing Wushu, Karate, Wing Chun, Tai Chi and Choy Lay Fut as well.
If you're interested in a learning a style that encompasses many of the techniques you see, check out Choy Lay Fut.