Dictionaries of the Scots Language (DSL) defines this as:
“used in children’s rhymes”
“stew or hash made from cold roast beef, vegetables and seasoning.”
Suffice to say, the origin is doubtful.
There are also many spelling variations. In Social Life of Scotland (1884), Charles Rogers writes:
“Twenty pints o’ strong ale, Twenty pint o’ sma’, Twenty pint o’ hinkie pinkie…”
And from A Country Schoolmaster (c.1800), James Shaw has:
“Ink, pink, sma’ drink, Het yill and brandy: Scud aboot the haystack: And you'll get sugar-candy”.
This Herald article (2014) shows it survives in the name of beer:
“Another seasonal brew is the Inkie Pinkie which is available during the summer months and tastes light and fruity”.
There is only one example for “stew or hash” in DSL, from Margaret Dods’ The Cook and Housewife’s Manual of 1826:
“Inky Pinky. Slice boiled carrots; slice also cold roast beef, trimming away outside and skins. Put an onion to a good gravy … and let the carrots and beef slowly simmer in this; add vinegar, pepper and salt”.
However, in October 1993 the Dundee Courier listed it amongst traditional Scottish dishes:
“Errol mutton pies and Dundee cake, inky pinky, skink and skirlie, rumblethump and crowdie-mowdie, Athole brose and heather ale…”
And in Diana Gabaldon’s A Breath of Snow and Ashes (2005), it features at a feast for Flora MacDonald (of Bonnie Prince Charlie fame):
“Food was beginning to be brought out, tureens of powsowdie and hotchpotch … Forfar bridies, inky pinky … dishes of coleannon, stovies …”
This Scots Word of the Week was written by Pauline Cairns Speitel, Dictionaries of the Scots Language https://dsl.ac.uk.