1st: Try turning the choke off sooner and hold the throttle open enough to keep the motor running. Some loading up upon initial start up is normal, but once started, warmed and cleared out it should not load up. Leaving the choke on for too long will make it load up much worse. It sounds like this is your situtation. When it dies after sitting, is it due to too low an idle rpm or loading up? Try adjusting the idle up a little (turn in the screw with the black knob on it on the left side of the carb while holding the throttle open slightly - in = higher idle, out = lower idle).
2nd: If it continues to load up while idleing or at low rpm and everything is in working order (float level set, reeds in good condition, airfilter clean and properly oiled etc) then your jetting is wrong. For starters, try turning the air screw out 1/2 turn, if some improvement is found try another 1/2 turn. If it got a little better, install a smaller pilot jet and put the air screw back to the standard setting.
Once properly set up the KX100 should be able to idle and be ridden at low rpm without loading up. I know because I just set up my wife's 03 KX100. She can ride slowly all day, stop and let it idle etc without fouling or loading up.
keep in mind that you should not let it idle for more than a few minutes, as there is no airflow through the rad and the motor can overheat. Unlike a car, the kx does not have a fan to provide air flow at idle.
good luck and post back with further questions/results.