Hi there, first we need to give you the lowdown on what is happening with your bike, which is a commmon problem covering the whole XT660 range.
The issue is that these bikes come restricted from the factory to comply with government emission rules. Their first approach to restriction is to virtually choke the bike, by using a snorkle on the filter and a constrictly intrinsecate air box.
In few words the bike is starved of air flow, therefore there are times that when on either high revolutions or the opposite way on very low revs once the engine is hot, fuel goes to the combustion chamber without enough air to combust so to speak and that is when the "choking" occurrs.
The Kev Mod was designed by Kev (who is an expert Volkswagen Engineer Foreman in Brisbane Australia) to trick the ECU by altering the send temp of the AF thus allowing more fuel into the mixture. Way back since 2006 when Kev first introduced this mod it has been very succesfull and everyone who fitted one has praised the simplicity and functionality of it.
In addition to the Kev mod it is recommended to fit a DNA stage 2(3) airbox cover filter, which opens up the airbox to the much needed air that will allow the bike to have the intended air influx. That, together with the Kev Mod or a more expensive powercommander will make this bike a high performing engine as intended by its designers.
You can see details about this side cover filter on the link below, this filter was designed by Dino Nikolaidis, MD of DNA Filters Ltd, in collaboration with us here at

specifically to modify / open up the airbox with a water tight safe to use high flow quality filter
http://www.xt660.com/site/node/324