Accessible is the word.

You can place a cover there and do whatever you want to camoflauge it as long as you can open it up without having to dismantle the finished surface. Texturing the wall plate to match the texture on the ceiling is one way.

The other option is that if one of the two lights is CLOSER to where it's fed from than the existing box is to pull the wire back to the box that light will be fed from and run a new wire to the second box and remove the original box and any remaining wiring.

What's above the kitchen? If you've got accessible attic above you don't need to preserve access from below.

ron-
In my area a plain junction box in the attic is not allowed, even if you can easily get to it. The inspector's rationale is that an attic junction box does not qualify as readily accessible because the box may not be readily seen, because it may be in a tight location, and/or it may be buried under insulation. When I've resorted to adding a junction box in the attic, I've run an unswitched feed to a box mounted off the attic floor - like on a rafter - and put a lamp base or receptacle on it to legitimize it. What's your view on this reading of the code?

I have a second floor above the kitchen, not an attic. Is there no other way to 'extend' this wire ? Do I really have to run a new one?

"The inspector's rationale is that an attic junction box does not qualify as readily accessible because the box may not be readily seen, because it may be in a tight location, and/or it may be buried under insulation."

Inspectors seem to like to make up their own definitions, even when the NEC definitions are perfectly clear.

'Accessible' means you can obtain access without damaging the finished surface.

'Readily accessible' means you do not lead ladders, etc. You can walk up to the item and access it.

A box does not have to be "readily seen" to be accessible.

Insulation is not a 'finished surface' so digging to find the box is not prohibited.

And "tight location" are a matter of convenience.
You are not working on a box that may still contain some live equipment (like a panel fed by a meter).
I have worked in plenty of cramped, hot, and wet locations (crawl spaces being one contender for lousy places to work).

Is there a higher state authority to complain to?
This guy sounds like a petty tyrant.

brickeyee-
I pretty much agree with you, and have had my own run-ins with inspectors that I thought were over the line. However, I have to admit that in some of the houses I've owned and worked on there have been junction boxes in attics that I found only by accident, after wasting a lot of time hunting down a problem. Inspectors do often have their own interpretation of the "bible," but, in this situation, I can see that it's not totally without merit....

"I have a second floor above the kitchen, not an attic. Is there no other way to 'extend' this wire ? Do I really have to run a new one?"

Sorry. Wire doesn't stretch. Anything you do to join another wire to this one would be a junction and would need to be in a junction box and follow the applicable rules.

You can either put a plate over it so it remains accessible or run new wire.