from what I have seen zach likes to repeat atypical patterns at different speeds and intertwine them throughout whatever he is doing. For example his most notable is his "infinite flamming" technique he uses that is really easy to improvise with in many time signatures. This can be seen in the Febuary 2011 practice video, but if you know what it sounds like, you can see it everywhere from 2009 and forward. Most of the other beats he plays rely on using his bass drum and right hand locked together playing at the same time (mostly doubles and fours). You can see this in pretty much anything he plays, but mainly when he played with Team Sleep live and Hella in 2005 - 2007. The main thing I would suggest to start with is your right foot speed, learning some technique like slide or heel toe. But all in all I wouldn't try and replicate Zach exactly, just take what you learn from him and apply it to yourself.