In  Highland Clansman 1689-1746 Stuart Reid  p 18 writes it is possible this banner was carried by one of the companies of the Earl of Cromartie's Regiment at Embo near Golspie

 
The Battle of Littleferry/Bonar Bridge/Skirmish at Golspie near Dunrobin 15th April 1746

The Battle of Littleferry/Bonar Bridge or the Skirmish at Golspie, south of Dunrobin 15th April 1746, the day before the Battle of Culloden was probably when the two Sinclairs in George Mackenzie, the 3rd Earl of Cromartie's Regiment were taken prisoner.

The 18th Earl of Sutherland supported the Government against the Jacobitesand raised a force against them, but disbanded them for the harvest in 1745, while the Jacobites were in the south. The Earl of Cromartie's force of around 500 took Dunrobin Castle in February and the Earl of Sutherland narrowly escaped capture. In April the Earl of Cromartie's Regiment was ordered to rejoin the main Jacobite force. Three independent companies of Government volunteers in the area, composed of Mackays and Sutherland Militia decided to unite attack them.

"In pursuance of this resolution, Captain Macallister, who commanded the Earl of Sutherland's militia, marched with his company towards the water of Golspie, and having in his march received intelligence that Cromarty's regiment had marched towards the ferry, but that the earl himself with the greater part of his officers was at Dunrobin Castle, he sent Ensign John Mackay, with a party of 26 men, to intercept him. The earl left the castle
with 14 officers on horseback, and a small party of well-armed foot, to join his men, and would have fallen into an ambuscade which Ensign Mackay had laid for him, had not some of the Mackays begun to fire too soon. Lord Cromarty immediately retraced his steps and took refuge in the castle, from the top of the tower of which he displayed a white flag and rang a bell, as a signal that he was attacked. The earl's men began immediately to march
back to his relief, upon which Mackay and his party retired to the adjacent high grounds. Meanwhile, the two independent companies, which were to attack Cromarty's men in flank, arrived at the hill of Culmaly, to the north west of Golspie, and observing the insurgents returning from the ferry, and drawn up in order of battle on a rising ground about a mile west from Golspie, they concealed themselves on the top of the hill: Captains Gray and
Sutherland, the commanders of the two companies, then descended the hill to reconnoitre. They computed Cromarty's force to be between 400 and 500 men; and, having resolved to attack them, they returned to their men and gave orders to that effect. To deceive the insurgents as to the extent of their numbers, they marched down the hill in open column, keeping a distance of about twenty paces between each rank; and so well did the ruse succeed, that the insurgents, struck with a panic, fled towards the ferry, and were pursued by the two companies, who, attacking them in flank, killed a considerable number, and took 178 prisoners. The two companies thereupon marched to Dunrobin castle, which they invested. The earl held out the castle till the evening, when, despairing of relief, he requested the commanders of the companies to hold a conference with him in the castle on the subject of surrender. While engaged in conversation, Ensign Mackay, who had entered the castle along with two captains, went down stairs, and having informed the earl's men below that he had surrendered, induced them to deliver up their arms. Having secured their arms, he took the keys from the porter, and, opening the gates, admitted his party. He then went up stairs with them, and, entering the dinning-room, seized the earl, Lord Macleod, and the whole officers."

The Earl of Cromarty was condemned to death for treason but later pardoned, but his title forfeit.

References:

Full text of "[Culloden papers] More Culloden papers"

Clan Sutherland History

The Earl of Cromarty in thePeerage.com

Dunrobin School History

Mackay Country Scottish Highlands

Clan MacKenzie Society in the Americas - The Earl of Cromartie - March 2008.