Troubles in the engine/adjustment part..

I see it's missing the word connection. I cut the spark wires, and put the caps back on with no results. Just ordered a dyna S kit with new coils, wires, caps and spark plugs

Good move. It couldn't work as is. The yellow/red wire comes from the kill switch and provides power to the coils.
Steve

One thing I did notice is that the battery only shows 5,5-6 volts. 
couldn't check with engine running since I just scrapped the ignition.
Starter does manage to get the engine turning properly.

Anyone have a explanation for this?

I have a 1980 KZ1000 that I converted over about a year ago.  Youi will need a Dyna S ignition setup and a set of 3.5 to 4 ohm coils.  The wiring is fairly simple.  You can eliminate your points, the igniter and the coils along with their ballast resistor.  

Be sure to get the correct Dyna system, as they have several for different bikes.  You want the Dyna S, advertised for big Kaw engines.

I ordered the whole from ClassicKawaParts.nl, a shop who has provided me with lots more.
Bought the kit with the dyna coils which are made for this set. So it should be good. Everything new and all dyna materials..

To the OP:  I do not have nor have I worked on a bike like yours, so what I have to say may/or may not apply.  The setup in your bike looks like something Rube Goldberg made up.  The designer may have had good intentions, but you don't know what they were or how it was supposed to work which inevitably leads to guessing which is almost never successful.  You are most assuredly going in the right direction with the Dyna S ignition.  However because your setup looks home brewed, I would make sure the point plate is the correct one for your bike and make certain the spark advance mechanism is also the correct one and WORKS PROPERLY.  If you are not certain about how that device functions just ask, but it must work properly for a good running motor.  You mentioned battery voltage being low, but just because you have enough energy to turn the motor over does NOT mean it will have enough energy to start the motor.  You would do very well to replace that battery with a new one.  A good battery is priceless when chasing engine or electrical problems on any vehicle.  If you don't have a battery charger/trickle charger get one.  This would also be a great time to start looking at wiring connections and grounds to make sure they are rock solid and corrosion free.  Good luck with your problem child.

Rick H.

wrote:

I ordered the whole from ClassicKawaParts.nl, a shop who has provided me with lots more.
Bought the kit with the dyna coils which are made for this set. So it should be good. Everything new and all dyna materials..

You can measure the resistance of your current coils if you have a multimeter.  You want to measure from plug to plug on each coil, with the plugs disconnected from the engine.  
 

So I finally made the call to stop trying on my own. I have done more than I could, and nothing is working. It had run for a bit, but is back to only one cilinder. 
I took the decision to bring the bike to Ruud Groeneveld, he has over 40 years of experience in classic bikes. He's gonna take the head of, redo the carbs again, and redo the ignition as well. I don't have a clue about what it is that's wrong, but time after time there is something wrong. 
So I have good hopes he can fix it, but am just a bit concerned about the costs.

Time will tell!
 

How did this turn out?

Not really as I wished. Bike is in basics good, after a lot of work. Valves, clutch, ignition, carbs etc all done. Technically it's in a good solid state. But it wouldn't run over 6000rpm, at freezing temps with open pods. I finally decided to buy K&N filters, and fitted them last weekend. Still tryingz and still hoping!