What's considered "saffron", come to kilts, is nothing like the color of the old "saffron shirt".
While I've no idea how the saffron color of the leine and the kilt compare, I do believe that it's a sure bet that it refers to the color, not the spice. Saffron is the dried stamens of the crocus flower; it's highly unlikely that there ever were enough crocuses blooming in Ireland for the entire nation to use it as a dyestuff when very, very few could even afford to use it as a spice.

Do any of you folks have any idea how that came to be?
In 1900 Seamas OCeallaigh of the Gaelic League asked Pádraig Pearse about developing an Irish national dress, perhaps based upon a pair of trews which had been found at Killery, County Sligo dated from about the 16th century in the Royal Irish Academy Collection in the National Museum in Dublin.

On October 26 Pearse wrote:
"...one would at first sight take them for a rather clumsily made and ill-treated pair of modern gentlemen's drawers. Frankly, I should much prefer to see you arrayed in a kilt, although it may be less authentic, than in a pair of these trews. You would if you appeared in the latter, run the risk of leading the spectators to imagine that you had forgotten to don your trousers and had sallied forth in your drawers."

The ancient dress of Ireland was the leine and brat, somewhat resembling a woman's chemise and a horse blanket. As a modern form of national dress, it suffers from the same limitations as the trews in the National Museum. As the Irish leine was traditionally dyed the color of saffron (the wearing of which had been banned by the English under Henry VIII in 1537), the color saffron was chosen as the color if the Irish kilt.