So, a couple things here: the myth of the American rifleman and different loads for black powder muskets.

Firstly, and very quickly, the American riflemen of the American War of Independence (AWI) are largely a myth. All major, decisive engagements were won or lost using European style warfare. Now, that warfare evolved over the course of the war, most notably using General Howe's light infantry tactics found in Howe's Light Infantry Manual and these tactics made their way back to Europe in time for the Napoleonic Wars and arguably opened the door for more radical light infantry like the riflemen. (See: "With Zeal and with Bayonets Only: The British Army on Campaign in North America 1775-1783" by Matthew H. Spring)

But, to answer your question more in depth, yes, cloth patches were used in flintlock rifles. To understand why we need to understand how black powder muskets work.

Black powder is a fairly weak explosive. It has a relative explosive factor (its explosive power in terms of its equivalent to TNT) of .55 meaning it is roughly half as powerful as TNT. For further reference, ammonium nitrate, the explosive used in the Oklahoma City bombing has an REF of .46 and C4 has an REF of 1.37. So in order for black powder to be effective you need a decent amount of it. Black powder also burns very inefficiently and leaves behind a sticky residue called "fouling" and once this fouling cools it dries rock hard, similar to how carbon builds up in a modern firearm but much faster. Because of this military muskets would be smooth bore (no rifling) and use smaller caliber balls. For example, the British Army's Land Pattern series of muskets, also known as the Brown Besses, had a .75 caliber bore but fired a .69 caliber ball. As the fouling coats the inside of the barrel and makes the inside tighter and tighter the private soldier was able to load and fire more rounds before the barrel becomes physically too small to fit another ball.

However, to hold the ball in place while the bore is clean and attempt to have the ball fly straighter, the soldier would use the paper from the cartridge as "wadding" to create more of a seal around the ball in the breech. The greased cloth you're referring to is also wadding. The paper wadding would burn off very quickly as the powder is ignited but a cloth patch would not.

For a rifle to work the ball needs to fit the barrel exactly so the grooves grip it and put the stabilizing spin on it. So in a rifle, military or civilian, you would patch your ball with something like wool, pure wool being mostly fireproof, that will create an even tighter seal around the ball, allow the forces to spin it, and put the ball where you are aiming.

More coming in the civilian sector, though, are smoothbore hunting muskets. In the 1750s the Canadien militia, the milicien, are using their hunting muskets, the fusil de chasse, which are smoothbore. Along with being more cost effective, these muskets allowed for a greater range of shot to be used. So single ball, bird shot, buck shots, buck-and-ball, etc can all be used in the same muskets. To make a single shot more accurate, the Canadiens would would use a caliber of ball that matches the bore and patch it with wool. This would result in a firearm with accuracy comparable to a modern, smoothbore shotgun.

So, to wrap it all up, yes. Riflemen of any nation would use cloth patches to wad their musket balls in order to make them effective. This would remain the practice until the invention of the Minié ball that would eliminate the need for wadding almost entirely.

I feel like I got too in detail on some things and may have left other details out by accident. If there's anything you'd like me to elaborate on please feel free to ask!

Edit: I confused the term "relative explosive factor" and "REF" for "net explosive weight" and "NEW." It has been corrected.