Correct. No example either.

afaict there's no audio clip for this, so i think it can be converted directly.

@@ -5,1 +5,1 @@
-<keb>一切気にしない</keb>
+<keb>気にしない</keb>
@@ -8,1 +8,1 @@
-<reb>いっさいきにしない</reb>
+<reb>きにしない</reb>
@@ -14,3 +14,2 @@
-<gloss>not give a damn</gloss>
-<gloss>not care a bit</gloss>
-<gloss>could care a less</gloss>
+<gloss>not caring</gloss>
+<gloss>not giving a damn</gloss>

I think just having an entry for 気にしない is sufficient. All those versions with amplifiers such as 少しも, ちっとも, 一切 and 全然 could probably be dropped.
気にしない has a subentry in 新和英中辞典 and is the gloss for a heap of entries in リーダーズ+プラス.
I guess it could argued that it's obvious as a negative of 気にする, and I presume that's why most JEs don't have it. I think it would certainly help text-glossing if it was be included.

if the 378 google hit entry was/is accurate, i don't think this should be an entry.  even if it gets far more hits, these are just standard meanings for 一切+気にしない.  you could say いっさい~ない for any verb, e.g. 一切食べない gets just as many hits as 一切気にしない
-
if anything, it should be converted to 気にしない, although i'm not certain that is needed as an entry either.
i also think the entries for 少しも-, 全然-, and ちっとも気にしない should be reconsidered
-
note: for whatever reason, i am incapable of recommending this entry for deletion.  the system craps out when that box is checked.  i think it's a rejected/deleted x-ref thing again

See below.

I am not making a submission about the above as such.
I searched for "気にしない" and I got the above entry. Then I clicked the link to "気にする". Then I could see that my search was the negative of the positive.

I know how that progression happened.

My point is this: Should there be an entry for "気にしない"?

Based upon what I believe you have stated before, there is no reason why there should be an entry for either the positive or negative. So, in my way of thinking, either there should be neither entry or there should be both entries [that would seem to be logic to me because if it were not for the nature of such an entry, normality would say that only "気" plus the [n,vs]classification would be normal].

If you agreed, the link in the above would be to "気にしない".

The following entries would carry the same logic:-

少しも気にしない 【すこしもきにしない】 (exp,adj-i) not give a damn; not care a bit
全然気にしない 【ぜんぜんきにしない】 (exp,adj-i) (ant: 気にする) not mind in the slightest; not give a damn; not care a bit
ちっとも気にしない 【ちっともきにしない】 (exp,adj-i) (See 気にする) not give a damn; not care a bit; could care a less

If you preferred, for some measure of clarity, I guess that you could include the “ant” in front of the link to all of the entries to which I have referred. However, the aspect which I think can cause an odd way of thinking with the existing entry for “気にする” is the negative nuance, ie., as shown below:-

気にする 【きにする】 (exp,vs-i) to mind (negative nuance); to care about; to worry; to pay undue (amount of) attention to (something).
Whereas, it seems to me that “気にしない” also, in context, has a positive nuance [ie., [please] don't worry [everything is fine] when said in response to an enquiry from someone who really cares.
Sorry to ramble on a bit, but fewer words, in my mode, may have failed to deliver the message.