2011 mini convertible misfire. Started with P300 and P301. Changed engine coil for cylinder 1 and all four plugs. Same issue now with P300,P303 &P304. Thoughts as to what to tackle next?

0339 is intermittand crank position pulses. That'll do it!
Check for bad connections/replace the sensor if faulty.

I'm assuming you mean codes P0300 and P0301. Black soot on the plugs is usually because the fuel system is running 'rich'. This is when the fuel/air mixture going into the engine has too much fuel in it. Changing the spark plugs was a good step to take but it won't fix the problem.
When was the vehicle last given a full service? Something as simple as an old, dirty air filter can cause problems.
If you are not familiar with working on engines take the vehicle to a good mechanic and get them to look at it for you.

P1399

Is it a 4 cylinder engine, and all four cylinders are misfiring?

Misfires will set a code when the computer senses a lag in power output from a cylinder, based on the input from the crank position sensor. Misfires are usually caused from a loss or a problem with gas, spark, or compression-one of those three is wrong for a misfire to occur. New coils and plugs, so probably not a spark problem-unless the spark timing is wrong-let's leave that for now. You should have the fuel pressure tested, and see if pressure is as specified. If pressure is low, and you have new filter, probably a weak pump.

Check cylinder compression as a last resort. Your lowest reading cylinder should be within 75% of the highest reading cylinder. A compression test is a good indicator of the internal health of the engine, the higher the compression, the more power output from that cylinder. But it should be even and balanced, lowest should be within 75% of the highest reading.

So, gas, spark, or compression?

Those P300 codes are cylinder misfires
from bad COP Ignition Coils

I don't think it is your catalytic converter because your light usually flashes and a bad cat I never heard of them causing a misfire. I ran your other code it is for a faulty EGR system. Exhaust gas recirculation excessive. You are getting too much exhaust gas back in the system. This will cause your misfire. Go-to a trusted mechanic and have them check out your EGR system.

this can be caused by a loose or worn camshaft belt.

Reset the computer.

http://www.kiatechinfo.com/index.asp

Good source for Kia its free to register NO STRINGS

Code p300 - random misfire
code p301 - testing and results
code p303 - misfire cylinder 3
code p306 - misfire cylinder 6

i love code questions!!! i'm so good in this!