I have not made anything like a permanent sling for my flintlock, but I make and use a hasty sling on it frequently in the field, particularly if I have to both carry the gun, and drag a deer out. A friend made a semi-permanent sling for his musket, 'tho'. He used a piece of tanned deerskin to wrap around the barrel, and under the ramrod. Then he sewed the two ends together, leaving a double tab to which he tied the ends of his sling. The back of the sling was another piece of deerskin that he wrapped around the wrist of his stock, and sewed into place, like the barrel wrap. He could move the barrel " sleeve " back and forth between two of the ramrod pipes, so he could clean and oil the barrel, to keep it from rusting under the leather sleeve, but the wrap around the wrist was not easily removed. He was working on that issue the last time I saw the gun at the club.
I use a simple loop over the wrist of the gun, and another loop over the barrel and forestock of my long rifle. The forward loop is locked in place by putting it between the stock and ramrod, and I carry the gun muzzle down for both safety and positioning it on my shoulder. I carry a length of leather boot lacing in my day pack to use for a sling when I need one. I use slip knots on both ends, so they can be tightened, and loosened easily, as well as adjusted for length, but will hold the lace in place for the period of time I need to sling the rifle.
Now that lace is not as nice a sling on my shoulder as my formal wide sling I have for other rifles that have swivels on them. Keep that in mind when determining what kind of sling to design for what you are going to do. I am rarely more than a mile or two from my car, So I don't have a long trek where I have to carry my gun on that sling. If I were doing a trek, I would make a much better and wider sling out of leather or webbing, to get there and back.