This is all still very fascinating and even more so because I know I'm not even going to try. I've done enough like that already to last me. But here are some more notes and observations.
While Daniel Boone did appreciate his elbow room, he would not have been out for the fun of it. In other words, there has to be a purpose behind the outing, although I realize the original post did state a purpose of sorts. One sort of has to put one's self in the frame of mind of what one is doing. Personally, my outings are generally of a "point to point" sort of thing. The object is to get on down the trail. While that is the simple part, it's probably also the hard part. One can easily cover, oh, maybe as much as twenty miles in a day, provided the weather and the local savages cooperate and the river isn't too high. Basically, you're going from either one settlement or frontier homestead such as my own ancestors lived in less than ten miles from where I was born, to another place just like it. You might be going for any number of reasons.
Here is where the problems turn up. Some of these things will be next to impossible to do today for several reasons. The authorities in some places frown on open fires and a fire was very important to a frontier traveler on foot. He would also have been armed, not necessarily with a rifle but at least with a "firelock." That's also frowned upon, even in the wild west that is the United States. However, the savages are not as hostile as they once were.
But the fire is still most important. That's how we avoid the necessity of the second blanket. Sleep close to the fire. Everything will smell of smoke eventually but that's better than the smell of kerosene (paraffin). It follows that a fire-making kit is likewise essential. But that's been mentioned several times.
While they probably would not have passed up a chance to take game, hunting would have eaten into the travel time and was not the object (but you forgot to bring your trade musket anyway). In all probability, the food, such as there was of it, would have been that which they brought along and it would have been early forms of lightweight trail food, mostly from corn but also dried and processed (18th century style) meat, plus tea and tobacco. Springs and fresh water abound in the southern Applachians even today, except where mining has changed things, so not much water would have actually been carried, though a small flask or water bottle might have been taken.
While Boone may have used horses, they were still expensive and not yet essential for transportation. Without them, everything would have been carried on their own backs. Probably, they used canvas or leather packs similiar to what contemporary soldiers would have used, plus a haversack and a bullet pouch. Inside would have been a cup or mug, perhaps a bowl and almost certainly some form of pot or boiler (but not a pot boiler). Something to boil water in is a most difficult thing to improvise, so they would have had a small one. Also a candle and candle holder or perhaps a lantern. The blanket was in there and probably a treated canvas ground sheet. And not much else.
Upon finding a good spot to spend the night, they may have gone to the effort of making a shelter, freely cutting anything they needed from the forest. That's another thing that's frowned upon today but that is how they got by without a tent. For all the shelter and fire building, they would have used their tomahawk, Indian fashion but probably manufactured in England. No doubt the same people are still making them. A small hand ax, sometimes called a "pocket ax," was considered just the thing to have for the next hundred and fifty years. Clearly they are still popular, if posts on this forum are anything to go by. Boone and his party would have had knives galore but they would have used their tomahawks for more things.
We would feel uncomfortable wearing their clothes as much as we would any other contempory clothes. Leggings of leather, loincloth, and a hunting shirt would have been normal wear and probably a felt hat in lieu of a fur cap, although southeastern Indians did make fur caps. He also probably wore an ordinary shirt and perhaps a waistcoat with sleeves, which in French is termed a "veste." Ordinary clothing would have been worn as long as it lasted and it probably would have been home made. On his feet, probably Indian moccasins and another pair in his pack but he knew about shoes, of course. He grew up just outside of Phildelphia, which had a population of over 40,000 in 1800 (London was over a million).
He would have managed without a compass and probably maps, too. While he was a pioneer, the countryside was covered with trails and already isolated farmsteads and settlements covered the land, although the Indians were troublesome in that part of the country until the 1790s. He would have also managed without many of the things we consider essential for a short walk in the park on Sunday afternoon. However, in due respect to one of the greatest travelers and adventurers of all time, let us assume he never left home without a pocket handkerchief.