Whether or not the bike is jetted to richly, I think that the reason you are having the problems is that you let the bike idle for five minutes with the choke on, like Big Lou and Old Guy said. Two stroke race bikes like your KX are not set up to idle (although you can adjust the bike to do so), and are not meant to have the choke on that long. Maybe 15 seconds like noted above.
I suspect that your bike is "loaded up" with fuel and oil in the lower end from the five minute idling and easy riding around in first gear. Because the choke is making the fuel mixture "richer" (increased amount of fuel/oil relative to the amount of air being pulled into the engine) leaving the choke on that long made the loading up problem worse. Same thing with extending idling. At low RPM's, like idling, there is not a sufficient volume of air moving through the engine, so some of the fuel/oil mixture is condensing on the sides of the lower end and pooling down there. Even when a bike is jetted properly, this happens to a (minimal) extent. The bike will smoke a little more and not run cleanly until the bike is "cleaned out". In other words, before the bike runs well after starting the engine, the excess fuel and oil in the lower end must be cleaned out. It sounds to me like this is your problem, whether or not it was contributed to by improper jetting. Here is how to clean the bike out:
Warm up the bike using the method Big Lou described. When you turn off the choke, you will have to "blip" the throttle occasionally to keep the bike from stalling. When the bike is warm, start riding it. Get it up into second gear and slowly open the throttle all the way. Your bike will probably be blowing a lot of smoke and oil out the exhaust, but don't worry about it, this is just the excess oil and fuel from the bottom end. Do this a few times and the bike should be "cleaned out" of the excess fuel/oil in the bottom end. At that point, it will probably smoke a bit when you twist the throttle, but nothing too heavy.
At that point, your bike will be cleaned out. That should cure your problem. If it still smokes excessively and runs poorly after you cleaned it out, then you may have to adjust the jetting in the carb. But don't cross that bridge until you have to.