Not being able to see the material and going on your description alone it could have been “Linsey-Woolsey” (i.e. home-spun wool) or a coarse linen, but, I have no documentary sources to offer.
The following is from the website of the King’s Royal Yorkers--Rev War Reenactors (link below). Although it does not address your question directly; I thought you’d find it informative.
One of the other particular duties that were performed by drummers was that of meting out punishment. Once an offender had been tried and found guilty, the troops would be formed into a hollow square to witness the punishment, the crime and sentence was read aloud to the troops, the offender was paraded in front of the ranks of soldiers to the tune of 'Rogues March' and then secured to a tripod made of halberds (pole arms). The drummers would flog (or whip) the bare back of the offender, rotating the job amongst those drummers present to ensure the punishment was executed consistently. The whip of choice was referred to as the 'cat of nine tails', a short-ish whip with nine flails. The 'Cat' came in many forms some considerably crueller than others. When not in use the 'Cat' was carried in a red silk bag by the drum major and when 'the cat was out of the bag' trouble was imminent. Drummers were paid extra money for performing flogging duty.
To Join the Company of Military Historians click here