Thick white smoke? oil is usual blue-ish, and running rich is black.... that is sometimes indication of water/moisture in the fuel... drain some fuel out of the line into clear jar, let it sit for about 5 minutes and look for phase separation. Oil level OK?
see if you can remove the air filter, and keep it running on brake parts cleaner/carb cleaner or starting fluid through the intake. Also provide the model number of the engine so we can see the set up.
https://www.jackssmallengines.com/jacks-parts-lookup/kawasaki-model-locator.aspx
had a generator one time, ran like the choke was on all the time, but blew white smoke, drained the fuel and there was water in the carb bowl and fuel tank. flushed the system and it was good 2 go.