Actually, the dust cap cannot sit flush with the head tube because it rotates with the handlebar. So every time you turn your handle it is going to grind against the tube, however smooth or light it is and pretty soon it will eat through the paint and start touching carbon. The gap has to be there, how much you are comfortable with is the question. You can take it to a bike shop and ask for advice, also look at brand name bikes which have ICR and similar dust cap situation. There is a slight gap that remains.
I had about 2mm of gap in exact same spot and no matter what I couldn't get rid of it. I see that you have not assembled the stem/spacer/handle yet. Suggest you to tighten the full assembly as if you are readying the bike to ride and then check the gap again. This was suggested to me by someone. I did that and still had a gap that looked ungainly. After back and forth emails with Chris the matter led to nowhere because that gap seemed okay to him... may be it is okay, who knows? It certainly looked too big to me so I started seeking help here and some other forums. All my "hacks" for this are written here in the past few pages.
Long story short, as per suggestion from a member here I took my bike to someone who has a vertical press type grinder (I don't know what it is called) and after some brainstorming, decided to shave off 0.8mm of material from underneath the dust cap. Not the whole bottom of the dust cap but just the part that rests on C-ring so basically keep the flange of the dust cap intact but remove some material within the flange. The other option was to find dust cap and C-ring combo that is slightly shorter in height, which I was not. It could be there but I wasn't able to find that would be a perfect fit for this frame. That is a problem with Chiner frames because you searching with frame model yields zero results on eBay, Amazon, AliEx or the likes.
I have circled the area in your picture that we grinded from the dust cap. I was advised here to not use any home made remedy, namely Dremel or angle grinder because it is near impossible to shave off material in that spot in perfectly flat manner. Its rather tricky.
You are right about the customer support. If it gets tricky like this, you are on your own. They just stop replying. There was no answer to play in the handlebar (while rocking the bike back and forth) but that is whole another chapter.
To summarize, tighten things to 100% and observe the gap, if its still too much look into dust cap modification OR you can find a dust cap/C-ring that are not as tall as what VB supplies. Its been a while, may be there is some headset that is better than VB's.