First realise K3s have a funny behaviour at cold starts. They either immediately rev over 3000 rpm or die. Train yourself playing that choke knob is the only you can do. Previous models didn't show this behaviour: after a cold start one could return the chokes to fully open within a few seconds and then keep the rpm at a steady 2000 either by the throttle grip or by the idle adjust knob for the first mile. Not so with the K3s. Has to do with the leaner running that was inforced from 1977 on.
Having said that, I consider it a good routine to check the ignition first. What ignition is on yours, conventional or other? When it runs, does it run on all fours?
Are breakerpoints properly gapped?
Is the timing right and does the advancer function OK? When the bike has been inactive for a long period of time, make sure the advancer moves smoothly and does not stick.
Arcing at the breakerpoints may indicate a faulty condenser.
Concerning the carbs. Do all 4 vent? Does fuel arrive unhampered in the float bowls? Any 'extra' fuel filter that may hinder flow? At what level have the floats been set: 12,5 or 14,5mm? You may perform a clear tube test to check the fuel level in the bowls. Level should be some 3mm below the flange.
What colour is the smoke? When it's black, see to it nothing obstructs the air intake. A forgotten cloth under the seat? When it's white smoke, any chance there is water in the fuel? Inspect the paper airfilter element. Is it wet and/or fouled by that breather element under it?
After you've made a number of posts - I forgot how many - this site allows you to upload video's so we all can see and hear.