At the John Knox Museum in Edinburgh there is displayed a flag called
the "Blue Blanket".  To what dies the "Blue Blanket" refer?

Hello thecapitalscot-ga

Thank-you for your question.

The "Blue Blanket" refers to a Scottish Craft banner of great antiquity.

"The craftsmen were given a banner by the King which the Queen,
personally, inscribed with a Saltire (St. Andrew's Cross), a thistle,
an imperial crown and a hammer as well as the following words: "Fear
God and honour ye King with a long Iyffe and prosperous reign and we
shall ever pray to be faithful for ye defence of his sacred Majesty's
royal person till death". The King decreed that the banner should be
called the 'Standard of the Crafts Within the Burgh'. This banner was
one of the first to use the thistle as a symbol of Scotland. The
banner affectionately became known as the 'Blue Blanket' from its
background
colour which reflects the background of the Scottish flag."

This quote comes from the following page which details the story of
the "Blue Blanket":
http://owmg.org/Education/STB/STB-1994/STB-JU94.txt

Further information can be located on this page (about a quarter of the way down):
http://thecapitalscot.com/faq_capscot.html

If you require any further assistance on this question, please ask for
clarification and I will do my best to respond swiftly.