Whenever a touch hole liner is talked about, the Chamber's White Lightnin' is almost always mentioned. It is one of the top recommended touch hole liners offered for fast reliable ignition of our flintlock guns.
Note: The final step of the White Lightnin' installation is to file off the slotted part of the liner to make the liner flush with the outside of the barrel. In short, Jim Chambers designed his touch hole liner so that after installation, it is not to be removed.
Some touch hole liners use a slotted end or an Allen head for installation. Just because those liners can be removed doesn't mean that they need to be removed. Little positive gain is obtained over a wipe with a pipe cleaner or dental brush pick by removing a touch hole liner. The drawback to frequent removal of the touch hole liner is wear on the threads in the barrel.
In my experience, I have no need to remove a touch hole liner except in the case of the touch hole burning out and becoming so oversize that accuracy falls off and 3f powder will auto prime the pan.
I do believe that the nipple on a percussion capped gun can and should be removed for cleaning. A nipple should not be tightened so tightly that the threads in the nipple seat are stressed. The anti seize or whatever lubricant will protect the threads from fouling. The drum should not be removed either. I do not recommend removing the "clean out" screw. The "clean out" screw is an artifact from manufacturing the breech plug or drum to ease the manufacture of the breech plug or drum. Yes, some drums have a lot of angles and use of then the boring access can become a "clean out" screw for better cleaning of the breech area. Leave the drum in place. Its just too difficult to get the nipple back in alignment with the hammer.
Now, if removal of the drum or touch hole liner makes you confident that you have cleaned your gun to the level of cleanliness that you want, then by all means do so. I am just expressing my 1 of 31,786 opinions no cleaning a muzzle loading firearm.