Facing
With a head tube it depends what the material is really. I tend to run a very fine but wide flat fine over the faces, just to remove any high spots, but as a headset is not subjected to any real rotational stress, its not that important.
HOWEVER
With King headsets, they do work differently to every other headset and there are a few things you need to know!!! The main difference is they do not use a steerer wedge, but the top race ring has an internal O ring and 45 degree "wedge ring" that centres the steerer in the set. for this to be effective, you need a lot of torque on the tension cap, if the headset faces are not true, then the bearings may stiffen part way through turning and loosen the upper race clamp ring. Also to achieve the higher torque, you must use either a starfangled insert of bolt through headlock, that goes right through the steerer, DO NOT use a Hope Head doctor or any similar device, as these tend to creep up the tube allowing the top race clamp to cut into the steerer tube, if left unattended, this can cause the steerer to snap! I've seen this happen on several occasions!!! U are warned!
Also do not use more than 10mm of spacers, preferably none, as this can also have the same effect, allowing flex in the race clamp and marking the steerer.
There is an after market wedge adapter kit you can get from the US, that converts a King to a wedge style, but it involves some careful work with a file on the race clamp.
Always face BB shell faces with a proper tool with modern HT2 X type external bearing cups, or they will not last, this is partially why they have a bad name as 99 percent of folks don't bother. The old Shimano BB's sq, octalink and all the ISIS, didn't need a face up as they were one piece self contained units.
Oh and don't ream the head tube, face yes, but don't ream, just check for any roughness and relieve with a little fine emery, Chris King cups are always a little undersize anyway and reaming can result in them being literally a hand push fit (NOT GOOD!) which could effectively right off our frame!