I have read Thomsen's report, and she stated "A flag of similar pattern has never been received by this laboratory and it is out of our area of expertise to comment on it." (She was commenting on the pattern, not the flag.) She noted (as did Mr. Malpass) that the rope in the pole sleeve was common in naval flags. The thread count in the tight weave was similar to six flags in TPA's database - one was post war, the others late war issue. The quotes from Thomsen's report set forth in the auction listing are word for word.

The Flags of the World article (linked below) shows the yellow/blue flag used for the letter "K" as far back as 1790.

My opinion isn't worth anything, but here it is - maybe the flag is what the seller wants it to be. The lack of provenance makes it a tough sale.