The 7th Foot, or Royal Fusileers, were garrisoned in Quebec at the start of the war. The greater part of the regiment was captured in the at Fort Saint-Jean (1775) and Fort Chambly (1775) in the first American offensive. The remainder of the regiment (63 men), served with distinction during the defense of Quebec (1775). The regiment was reconstituted at New York in the winter of 1776-1777 following prisoner exchanges. The 7th was present for the attacks on Fort Clinton (1777) and Fort Montgomery (1777) and was stationed in Philadelphia for the winter of 1777-1778. Over the following 2 years, the regiment participated in the battle of Monmouth (1778) and William Tyron's Connecticut raid (1779). The following year, the 7th accompanied Henry Clinton's expedition to South Carolina, and participated in the siege of Charleston (1780). At the conclusion of the siege, the 7th was placed in garrison at Charleston, joining Charles Cornwallis' field army after the battle of Camden (1780). The 7th was later intended to be garrisoned at Ninety-Six, South Carolina, but was instead diverted to assist Banastre Tarleton's pursuit of Daniel Morgan. Subsequently, the regiment was captured at Cowpens (1781). It is believed that some men of the 7th continued to serve with Cornwallis after Cowpens; these men would have been captured at Yorktown (1781). The regiment was reformed in later years and was stationed in Charleston and Savannah before those towns were evacuated. According to Johann Ewald, it was one of the last four British regiments to depart New York in November, 1783 (the others were the 22nd, 23rd, and 40th regiments).
According to Tarleton, the regiment was made up of "chiefly recruits," at the time of Cowpens, which caused problems on the battlefield (early in the fight, he reported, it was necessary to put a stop to "a fire from some of the recruits of the 7th regiment"). Lieutenant Roderick Mackenzie of the 71st Foot, however, extolled the Fusileers for having "attained the summit of military discipline." Neither description is wholly reliable. Tarleton's narrative was written at a time after the war when his reputation was under attack; Mackenzie accused Tarleton of slighting the men under his command to mitigate his own culpability. Mackenzie, however, loathed Tarleton, and was not above stretching the truth if it would do his former commander injury.
In a dramatic painting, Don Troiani portrayed the moment at which Lieutenant-Colonel John Eager Howard’s Continentals captured the colors of the 7th Foot at the battle of Cowpens. This is, to the best of my knowledge, the only instance of a British regiment losing its colors on a battlefield during the Revolution (if only because flags were sometimes left behind).
The website of the recreated 7th Foot has a transcription of a letter from Brigadier-General Daniel Morgan to Samuel Huntington, president of the Continental Congress, that seems to confirm that the flags were taken during the battle itself. It states, in part, that he is sending to Huntington, "the standard of the 7th British Regt, which fell into my hands in the action of the 17th Jany – the other that was taken at the same time, I believe fell into the hands of some of the Militia." This suggests that one of the flags was taken by, or surrendered to, the Continentals, while the other was captured in some manner by the militia. At the time of the letter, Morgan didn't know what had become of the flag that the militia captured, because when the battle ended he was so caught up with other matters that "a proper inquiry could not be made after it."
Philip R. N. Katcher (1973). Encyclopedia of British, Provincial, and German Army Units 1775-1783. Stackpole Books.
There are two recreated versions of the 7th Foot: here and here. Both have informative websites.
This website is a wonderful resource for all things related to Banastre Tarleton, and includes transcriptions of Tarleton's memoir and Mackenzie's Strictures.