If you are going to do this, just inverting the forks and pumping oil out will not get all the crud out of the bottom. And when you wash out with kerosene without taking springs out, you will never get the fork oil level right even if you have caught and measured the oil you removed before washing out.
Every 1mm of fork oil level is a little less than 2ml of fork oil so you can very easily be half an inch out and that would affect your suspension a lot.
You will have to have the help of a STRONG assistant and buy two tools.
There is a spring compressor:
and a damping rod holder:
Do not buy the 4 in 1 damping rod holder. It has too much recess on the adapter thread and you will not be able to reassemble the fork unless you and your assistant are built like gorillas.
Both these can be bought from Traxion Dynamics or Motion Pro and cheapies on Ebay are available. Both should cost you less than an hours labour from your stealership. If a B-King specific tool is not listed, get the Gen 2 Hayabusa variant. You do not need the "fork oil measuring tool". Just use a ruler inserted into the fork leg like a dipstick.
I guess a dealer would charge 3 hours for the job, so with the money you save, get an Abba swingarm pivot stand as well. They are made in England and quite reasonable from Demon Tweeks.
Not having the Abba, I used two long 12mm bolts inserted into the swingarm pivot and carefully lowered the bike and bolts off my paddock stand onto two car axle stands. I then used a jack under the exhaust headers so that I could get the front wheel off the ground for removal. The King is nearly 50/ 50 weight distribution so you will not damage the headers with too much pressure.
The headlamp will have to be dropped forward to get to the top fork pinch bolts. Also make sure that you have set the preload to minimum and rebound damping to minimum.
Loosen top fork pinch bolts first and then loosen fork caps (much easier than trying to do once forks are off the bike).
Be careful with your selection. See the following table and how labeled viscosities are all over the place compared to actual viscosity (at 40 deg C - not important are the hot viscosities - they are important for rear shock oils).
The B-King manual specifies "LO1" oil. On the chart in the link, you will see it has a viscosity similar to from labeled 2.5 weight to 10 weight brands of oil. I chose a slightly thicker Motorex Racing Fork Oil 5W as I have put stiffer springs in and wanted to be sure of rebound damping control, but the Motorex 2.5W looks spot on with the specified OEM. I would not put thicker oil than I have in (Viscosity 22) as small bump compression damping is starting to get a bit harsh.
It is very tough pushing down on the spring compressor so that you can get the forked tool under the damper rod nut.
When you reassemble, turn the damper rod nut a few mm's higher than the specified 11mm of thread from the top of the nut to the top of the damper rod. This will make it a lot easier to get the forked tool back in under the nut and you can then turn the nut back down again until 11mm is reached. Do this accurately on each leg or you will have different number of click stops on each leg afterwards from what stock is.
The height of the fork oil without the spring in and fork compressed with damper rod down is 100mm from the top of the fork leg.
The manual mentions 527ml oil but this is what Suzuki recommends you put into the leg when you are pumping the oil covered damper rod to get rid of bubbles. When you set the height to 100mm you will be pouring oil out. A 1 litre bottle has about a 100ml left when you are finished.
Springs go back with tighter windings to the bottom.
The specs and procedures are covered in the workshop manual you can download here.
Also, when you put the forks back, I recommend you raise them 12 mm through the top yolk. This will lower the front a bit and quicken the steering. I have been up to 270 kph on a slightly bumpy road and had no instability issues either.
To align the forks, tighten one enough to hold and then just pinch the bolts on the other. Slip a lightly greased axle through and if it turns easily, they are aligned. If not, squeeze the pinched leg up or down until aligned. Even a half mm out will show up as a binding axle.
I would not repeat this job in a hurry. Do not underestimate how tough it is to get the springs compressed.
I think Suzuki got the fork oil right and the whole front end is pretty good for what the bike is. The springs are on the soft side. Static sag is about 60mm when new and increases to about 75mm after a few thousand kilometres which is really pushing the wrong end of ideal setup but not as bad as many bikes I have seen. However fork oil and air gap tweaking is not really recommended to try and fix this.
If you are a heavier rider AND want to get stiffer springs, the end result of doing all this is quite nice. I now have a static sag of about 50mm (can't remember the exact values but they were basically 20mm better all round) and unless I hit a pothole at speed, always have about 5 -10mm of travel left. Before just heavy breaking bottomed the suspension. The progression on the Wilbers springs is also different and although stiffer, still smooth and comfortable. I have made a good front end better which was worth all the trouble to me.
I have tried to remember all the practical tips that the manual does not give you.