A Note on Livery Colours
Livery colours are normally of the principal tinctures of the arms. The pinsel illustrated is that of the Laird of Gayre and Nigg whose pronominal arms (shown right) are Argent a fleur-de-lys Sable, in dexter chief a mullet Vert for difference. Hence his livery colours would normally be silver and black (although he actually used silver and green, the colour of the small mullet).
The full quotation from the Lyon Office leaflet is as follows ~

The Pinsel

This is the flag denoting a person to whom a Clan Chief has delegated his authority for a particular occasion, such as a Clan Gathering when the Chief himself is absent, in a word, the flag of the Chief's representative. It is triangular in shape, 2 feet high at the hoist and tapering to 4 feet 6 inches in width, with a background of the main livery colour of the Chief's arms. On it is shown the Chief's crest, within a strap of the second livery colour and buckle (gold for full Chiefs), bearing the motto, and outside the strap and buckle a gold circlet (outlined in green if the background is not a contrasting colour to gold) inscribed with the Chief's or Baron's title. On top of this circlet is set the owner's coronet of rank or his baronial cap. In the fly is shown the owner's plant badge and a scroll inscribed with his slogan or motto. This flag is allotted only to Chiefs or very special Chieftain-barons for practical use, and only upon the specific authority of the Lord Lyon King of Arms.

However, the apparent contradiction here is resolved by the associated paragraph in SCOTS HERALDRY by Sir Thomas Innes of Learney, Lord Lyon King of Arms, which states ~

The Pinsel

This is a triangular flag, 4ft 6 ins long by 2ft high, containing the crest within a strap (of the principal charge) and buckle (gold for full chiefs), bearing the motto, and within a gold circlet (if necessary fimbriated vert) inscribed with the chief's or baron's title, and ensigned with coronet or cap. In the fly is the plant badge and a scroll of the slogan or motto. This flag is used by a Chief's Tosheador or local Commander exercising his authority in his Chief's absence. Given only to Chiefs or very special Chieftain-barons for practical use.

So the strap on the illustrated pinsel is black, the colour of Gayre's fleur-de-lys.